Book of Abstract Symposium on Biomathematics 2018 · Model and Its Impact on Public Health...

Book of AbstractSymposium on Biomathematics 2018

Depok, Universitas Indonesia31 August � 2 September 2018

CONTENTS

COVER................................................................................................... i

CONTENTS ............................................................................................ ii

PLENARY TALK ..................................................................................... 1

PT 001: From In�situ Host�Seeking data to continuous malaria modelling .......... 1

PT 002: A Problem in Selecting between Human Mobility and Migration Model in

Dengue Disease Transmission ................................................................. 2

PT 003: .................................................................................................. 3

PT 004: Chaos Via Torus Destruction in Population Biology and Its Implications

for Data Analysis.................................................................................. 3

PT 005: Bioinformatics, Big Data and Precision Medicine ................................. 5

PT 006: Modeling the Implementation of Dengue Vaccine: The History Behind the

Model and Its Impact on Public Health Practical Intervention ......................... 6

INVITED TALK ....................................................................................... 8

PT 007: .................................................................................................. 8

IT 001: Global Stability of A Discrete SIR Epidemic Model with Saturated Inci-

dence Rate .......................................................................................... 9

IT 002: A Comparison of Fuzzy Clustering Approaches for Gene Expression Profil-

ing in Advanced Breast Cancer after Neoadjuvant Chemo-and Hormone Therapy 10

IT 003: From Data to Drug Decisions: How Precision Medicine Can Help Solve

Real World Problems ............................................................................ 11

IT 004: Smart Probe for Intracellular Imaging: Lets Tame It! .............................. 12

IT 005: Modelling Commuter Data for Dengue in Jakarta .................................. 13

IT 006: Analysis of Mathematical Model of HIV�1 Infection in CD4+T Cells Due

to Cells to Cells Contact with Antiretroviral Treatment ............................... 14

Symposium on Biomathematics 2018, Department of Mathematics, Universitas Indonesia.

ii

IT 007: Indonesian Mangroves Extract Library: an Ideal Model towards Integration

of Indonesian Biodiversity Information System ........................................... 15

IT 008: ................................................................................................... 16

IT 009: Analysis of Multimodal Data using Fundus Images and Gene Expression

Data to Diagnosis of Diabetic Retinopathy ................................................. 16

IT 010: ................................................................................................... 17

IT 011: On Modified Logistic Growth Model .................................................. 17

IT 012: ................................................................................................... 18

IT 013: Having Fun with S�I�R Model ........................................................ 18

CONTRIBUTED TALK ............................................................................. 19

ID 001: Leptospirosis Disease Model: Seasonal Variation of Bacterial Population ... 20

ID 002: Modelling The Number of New Pulmonary Tuberculosis Cases with Geo-

graphically Weighted Negative Binomial Regression Method ......................... 21

ID 003: Numerical Analysis of The Impact of Loss�sight and Undetected Cases

in The Spread of TB .............................................................................. 22

ID 004: Mathematical Analysis of a Tuberculosis (TB) Transmission Model with

Vaccination in an Age Structured Population .............................................. 23

ID 005: Mathematical Models for The Dynamics of The HIV with Antiretroviral

Treatment Interventions and The Effect of Apoptosis on T�Cells ................... 24

ID 007: The Utilization of Optimal control on the HIV-1 Infection in CD4+ T Cells

with RTI and PI Therapy ........................................................................ 25

ID 008: The Importance of Social Interaction Factors on The Type 2 Diabetes

Mellitus Prognosis Model ....................................................................... 26

ID 010: Mathematical Model of the Effect of Bears on the Pacific Salmon Popula-

tion in British Columbia ......................................................................... 27

ID 011: Real�Time Dengue Forecasting by the Method of Analogues .................. 28

ID 012: Plasmodium Classification on Red Blood Cells Image using Multiclass

Support Vector Machines ....................................................................... 29


iii

ID 013: A Stage�structure Predator�prey Model with Ratio�dependent Func-

tional Response and Anti-predator ............................................................ 30

ID 014: Leslie�Gower Predator�Prey Model with Stage�Structure,

Beddington�DeAngelis Functional Response, and Anti�Predator Behavior ..... 31

ID 015: Sensitivity and Stability Analysis of SEIR Epidemic Model with Information 32

ID 016: Evolutionary Dynamic of Insecticides Resistance in two�locus of Anophe-

les Mosquitoes ..................................................................................... 33

ID 017: A Biclustering Procedure Using BicBin Algorithm for HIV�1 Human

Protein Interaction Database in NCBI ....................................................... 34

ID 018: Implementation of Factor Analysis for Bicluster Acquisition: Sparseness

Projection (FABIAS) on Microarray of Alzheimers Gene Expression Data ........ 36

ID 019: Dynamical Analysis of a Tumor Growth Model Involving Interferon Gamma 37

ID 020: Effect of Host Mobility in Dengue Dynamical Model Inter-two cities ........ 38

ID 021: Finding Correlated Bicluster from Gene Expression Data of Alzheimer

Disease Using FABIA Biclustering Method................................................. 39

ID 022: Biclustering Protein Interactions between HIV-1 Protein and Human Pro-

tein Using LCM-MBS Algorithm ............................................................. 40

ID 023: A Dynamical Model of Invisible Wall in Mosquito Control ..................... 41

ID 024: A Deterministic Model for Influenza Transmission of Two Strains with

Antibody Dependent Enhancement (ADE) ................................................. 42

ID 025: POLS Algorithm to Find a Local Optimum Bicluster on Interactions be-

tween HIV�1 Proteins and Human Proteins ............................................... 44

ID 026: A Competition between Javan Rhinos (Rhinoceros Sondaicus) and Javan

Bulls (Bos Javanicus) Model with Allee effect ............................................ 46

ID 027: Gene Co�expression Network of Alzheimers Gene Expression................ 47

ID 028: On The Risk of Zika Virus Infection for Travelers ................................. 48

ID 029: MARS and Bagging MARS in Stroke ................................................. 49

ID 030: Epidemic Model of Co�infection of Dengue and Chikungunya................ 50


iv

ID 031: Imitation Game Dynamics on Vaccine�Decision Making Behaviour on

Dengue Transmission Dynamics .............................................................. 51

ID 032: Exploration on Virus Transmission using Complex Networks: Pandemic

Flu in Los Angeles ................................................................................ 52

ID 033: Optimal Fish Harvesting Strategy using Forward�Backward Sweep Method 53

ID 034: Mathematical Model of PI3K/AKT Pathway in The Absence of Protein

Phosphatase in AML ............................................................................. 55

ID 035: Performance Comparison of the Convolutional Neural Network Optimizer

for Photosynthetic Pigments Prediction on Plant Digital Image ....................... 56

ID 036: Mathematical Model of Dengue Transmission with Mobility Aspect ......... 58

ID 037: The Helicoverpa Armigera Spread Controlling Model on The Glycine Max

Growth using Zea Mays L ...................................................................... 59

ID 038: SIR�SI Model for Malaria Disease with Treatment and Vector Control ..... 60

ID 039: Modeling of Rabies Transmission Dynamic between Human and Dogs

with the Effect of Immunocontraceptive Vaccine ......................................... 61

ID 040: Mathematical Model of Zika Virus Transmission with Saturated Incidence

Rate ................................................................................................... 63

ID 041: Modeling The Spread of Bacterial Resistance in Hospital........................ 64

ID 042: Blighted Ovum Detection Using Deep Convolution Neural Network Method 65

ID 043: Mathematical Model for Rise and Fall Army Population ......................... 66

ID 044: Stability of Hepatitis B Virus Model with Cure and Absorption Effect ....... 67

ID 045: Optimal Control of Innate Immune Response in Infected

Lung�Macrophages by Streptococcus Pneumoniae ..................................... 68

ID 046: Parameter Estimation of External Forced Oscillation of Fuzzy Duffing

Equation: Numerical Performance by Extended Runge�Kutta Method ............ 69

ID 047: Global Stability of The Disease Free Equilibrium in A Cervical Cancer

Model: A Chance to Recover .................................................................. 71

ID 048: Minimizing Parameter and Dynamical Uncertainties in Biological Models . 72


v

ID 050: A Fuzzy Basic Reproduction Number for A Fuzzy Smoker Growth Model . 73

ID 051: Protein Sequence Analysis of The Zika Virus and The Dengue Virus Using

Smith Waterman Algorithm .................................................................... 74

ID 052: Mathematical Modeling of Panama Disease Infection inside Banana Leaves 76


vi

Schedule of SYMOMATH 2018 Savero Hotel, 31st August – 2nd September 2018

Friday, 31st August, 2018

Time Activity PIC Room 08.00 – 09.00 Registration Organizing committee Lily 09.00 – 09.20 Opening from the Dean of Faculty of

Mathematics and Natural Sciences, Universitas Indonesia

Dr. rer. Nat. Abdul Haris Lily

09.20 – 09.30 Opening from Chair of Committee Dr. Dipo Aldila Lily

09.30 – 10.00 Photo session and Coffee Break Lily

10.00 – 10.50 Presentation from 1st Keynote speaker Prof. Heikki Haario Lily

10.50 – 13.00 Lunch Restaurant 13.00 – 13.50 Presentation from 2nd Keynote speaker Prof. Edy Soewono Lily

14.00 – 16.00 1st Parallel session Asoka, Lily and Peony 16.00 – 16.30 Coffee Break Lily

Saturday, 1st September 2018

Time Activity PIC Room 09.00 – 10.00 2nd Parallel Session Asoka, Lily and Peony 10.00 – 10.20 Coffee Break Lily 10.20 – 11.10 Presentation from 3rd Keynote speaker Prof. Thomas Goetz Lily 11.10 – 12.00 Presentation from 4th Keynote speaker Prof. Nico Stollenwerk Lily 12.00 – 13.30 Lunch Restaurant 13.30 – 14.20 Presentation from 5th Keynote speaker Prof. M. Asif Khan Lily 14.30 – 16.10 3rd Parallel Session Asoka, Lily and Peony 16.10 – 16.50 Coffee Break Lily 18.30 – 21.00 Gala Dinner Lily

Sunday, 2nd September 2018

Time Activity PIC Room 09.00 – 10.40 4th Parallel Session Asoka, Lily and Peony 10.40 – 11.00 Coffee Break Lily 11.00 – 11.50 Presentation from 6th Keynote speaker Maira Aguiar Ph.D. Lily 11.50 – 12.40 Presentation from 7th Keynote speaker Prof. Hiromi Seno Lily 12.40 – 12.50 Closing Dr. Dipo Aldila Lily 12.50 – 14.00 Lunch Restaurant

Schedule for Parallel of

SYMOMATH 2018

31st August – 2nd September 2018

Savero Hotel, Depok, Indonesia

Date : 31 August 2018

Time : 14.00 - 16.20

Room : Asoka

Chair : Dr. Sutimin

Time ID Number Author Title

14.00 – 14.20 Invited Talk 6 Sutimin, R. Heru Tjahjana and Sunarsih

Analysis of Mathematical Model of HIV-1 Infection in CD4+T Cells Due

to Cells – to – Cells Contact with Antiretroviral Treatment

14.20 – 14.40 30

Edwin Setiawan Nugraha, Karunia Putra Wijaya, Thomas Götz, Nuning Nuraini and Edy

Soewono

Epidemic model of co-infection of dengue and chikungunya

14.40 – 15.00 10

Jane Sahetapy-Engel, Azhary Ramadhanty, Eduardus Axel

Wijaya, Dancent Sutanto, Ambar Winarni and Prama

Setia Putra

Mathematical Model of the Effect of Bears on the Pacific Salmon

Population in British Columbia

15.00 – 15.20 14 Umu Salamah, Agus Suryanto

and Wuryansari Muharini Kusumawinahyu

Leslie-Gower Predator-Prey Model with Stage-Structure, Beddington-

DeAngelis Functional Response, and Anti-Predator Behavior

15.20 – 15.40 13 Adina Apriyani, Isnani Darti and Agus Suryanto

A Stage-structure Predator-prey Model with Ratio-dependent

Functional Response and Anti-predator

15.40 – 16.00 16 Dani Suandi, Edy Soewono and Kuntjoro Adji Sidarto

Evolutionary Dynamic of Insecticides Resistance in two-locus of Anopheles

Mosquitoes

16.00 – 16.20 37 Sri Intan Lestari, Juni Wijayanti Puspita and Rina Ratianingsih

The Helicoverpa Armigera Spread Controlling Model on The Glycine

Max Growth using Zea Mays L


Time : 14.00 - 16.20

Room : Lily

Chair : Dr. Setia Pramana


14.00 – 14.20 Invited Talk 2 Setia Pramana

A Comparison of Fuzzy Clustering Approaches for Gene Expression

Profiling in Advanced Breast Cancer after Neoadjuvant Chemo-and

Hormone Therapy

14.20 – 14.40 29 Ria Dhea Layla Nur Karisma and Sri Harini MARS and Bagging MARS in Stroke

14.40 – 15.00 1 Rudianto Artiono and Budi Priyo Prawoto

Leptospirosis Disease Model: Seasonal Variation of Bacterial

Population

15.00 – 15.20 12 Soya Febeauty Yama Otantia

Pradini, Alhadi Bustamam and Zuherman Rustam

Plasmodium Classification on Red Blood Cells Image using Multiclass

Support Vector Machines

15.20 – 15.40 18 Theresia Wutun, Alhadi

Bustamam and Titin Siswantining

Implementation of Factor Analysis for Bicluster Acquisition : Sparseness

Projection (FABIAS) on Microarray of Alzheimer’s Gene Expression Data

15.40 – 16.00 21 Nuning Setyaningrum, Alhadi


Finding Correlated Bicluster from Gene Expression Data of Alzheimer Disease Using FABIA Biclustering

Method


Time : 14.00 - 16.00

Room : Peony

Chair : Dr. Maulana Bachtiar, Dr. Samira


14.00 – 14.20 Invited Talk 3 Maulana Bachtiar From Data to Drug Decisions: How Precision Medicine Can Help Solve

Real World Problems

14.20 – 14.40 Invited Talk 4 Dr. Samira Smart probe for intracellular imaging: Let’s tame it!

14.40 – 15.00 27 Nyoman Arda Wibawa, Alhadi


Gene Co-expression Network of Alzheimer’s Gene Expression

15.00 – 15.20 43 Anita Triska, Heni Widayani and Nuning Nuraini

Mathematical Model for Rise and Fall Army Population

15.20 – 15.40 17 Patuan Pangihutan Tampubolon and Alhadi Bustamam

A Biclustering Procedure Using BicBin Algorithm for HIV-1 Human Protein Interaction Database in NCBI

15.40 – 16.00 45 Usman Pagalay, Dewi Zumrotul Nafisa and Heni Widayani

Optimal Control of Innate Immune Response in Infected Lung-

Macrophages by Streptococcus Pneumoniae

Date : 01 September 2018

Time : 09.00 – 10.00

Room : Asoka

Chair : Dr. Dipo Aldila


09.00 – 09.20 Invited Talk 5 Dipo Aldila, Nathania, Prama Setia Putra

Modelling commuter data for dengue in Jakarta

09.20 – 09.40 2 Tsuraya Mumtaz and Agung Priyo Utomo

Modelling The Number of New Pulmonary Tuberculosis Cases With Geographically Weighted Negative

Binomial Regression Method

09.40 – 10.00 52

Mochamad Apri, Husna Nugrahpraja, Mudita Gunawan,

Gandhiano Putera, Monica Reynata Sulaeman, Marcelino Wijaya and Joanne Immanuela

Rachman

Mathematical Modeling of Panama Disease Infection inside Banana

Leaves


Time : 09.00 – 10.00

Room : Lily

Chair : Prof. Agus Suryanto


09.00 – 09.20 Invited Talk 1 Agus Suryanto Global stability of a discrete SIR epidemic model with saturated

incidence rate

09.20 – 09.40 19 Intan Tamsih, Trisilowati Trisilowati and Ummu Habibah

Dynamical Analysis of a Tumor Growth Model Involving Interferon

Gamma

09.40 – 10.00 44 Lisa Risfana Sari and Puji Andayani

Stability of Hepatitis B Virus Model with Cure and Absorption Effect


Time : 09.00 – 10.00

Room : Peony

Chair : Alhadi Bustamam, Ph.D


09.00 – 09.20 Invited Talk 9 Alhadi Bustamam To be announced later

09.20 – 09.40 51 Mohammad Syaiful Pradana and Siti Amiroch

Protein Sequence Analysis of The Zika Virus and The Dengue Virus Using Smith Waterman Algorithm

09.40 – 10.00 42 Feni Andriani and Iffatul Mardhiyah

Blighted Ovum Detection using Deep Convolution Neural Network Method


Time : 14.30 - 16.50

Room : Asoka

Chair : Dr. Fajar Adi-Kusumo


14.30 – 14.50 47 Lina Aryati, Tri Sri Noor Asih, Fajar Adi-Kusumo and Mardiah

Suci Hardianti

Global Stability of The Disease Free Equilibrium In a Cervical Cancer

Model: A Chance To Recover

15.10 – 15.30 39 Eti D. Wiraningsih and Asep K. Supriatna

Modelling of Rabies Transmission Dynamics Between Human and Dogs

With The Effect of Immunocontraceptive Vaccine

15.30 – 15.50 24 Hilda Fahlena, Edy Soewono and Nuning Nuraini

A Deterministic Model for Influenza Transmission of Two Strains with Antibody Dependent Enhancement

(ADE)

15.50 – 16.10 11 Afrina Andriani Br Sebayang,

Mochamad Apri and Edy Soewono

Real-Time Dengue Forecasting by the Method of Analogues

16.10 – 16.30 36 Muhammad Fakhruddin, Nuning Nuraini and Edy

Soewono

Mathematical Model of Dengue Transmission with Mobility Aspect

16.30 – 16.50 50 Herlinda Nurafwa Sofhya and Agus Yodi Gunawan

A Fuzzy Basic Reproduction Number For A Fuzzy Smoker Growth Model


Time : 14.30 – 16.50

Room : Lily

Chair : Dr. Kholis A. Audah


14.30 – 14.50 Invited Talk 7 Kholis A. Audah To be announced later

15.10 – 15.30 31 Meksianis Ndii, Nursanti Anggriani and Asep Supriatna

Imitation Game Dynamics on Vaccine-Decision making Behaviour on Dengue Transmission Dynamics

15.30 – 15.50 41 Nela Rizka, Mochamad Apri and Pratiwi Wikaningtyas

Modeling The Spread of Bacterial Resistance in Hospital

15.50 – 16.10 33 Nailul Izzati and Imamatul Ummah

Optimal Fish Harvesting Strategy using Forward-Backward Sweep

Method

16.10 – 16.30 22 Olivia Swasti and Alhadi Bustamam

Biclustering Protein Interactions between HIV-1 Protein and Human

Protein Using LCM-MBS Algorithm

16.30 – 16.50 25 Tesdiq Kaloka and Alhadi Bustamam

POLS Algorithm to Find a Local Optimum Bicluster on Interactions

between HIV-1 Proteins and Human Proteins


Time : 14.30 - 16.30

Room : Peony

Chair : Prof. Asep K. Supriatna


14.30 – 14.50 Invited Talk 10 Asep K. Supriatna Mathematical model in Epidemiology

15.10 – 15.30 46

Muhammad Ahsar Karim, Agus Yodi Gunawan, Mochamad Apri Apri and Kuntjoro Adji

Sidarto

Parameter Estimation of External Forced Oscillation of Fuzzy Duffing Equation: Numerical Performance by

Extended Runge-Kutta Method

15.30 – 15.50 34 Yudi Ari Adi, F Adi-Kusumo and L Aryati

Mathematical Model of PI3K/AKT Pathway in The Absence of Protein

Phosphatase in AML

15.50 – 16.10 26 Respati Mentari and Eric Harjanto

A competition between Javan Rhinos (Rhinoceros Sondaicus) and Javan Bulls (Bos Javanicus) model with

Allee effect

16.10 – 16.30 8 Rina Ratianingsih, Hajar Hajar and Agus Indra Jaya

The Importance of Social Interaction Factors on The Type 2 Diabetes

Mellitus Prognosis Model

16.30 – 16.50 48 Levina Michella and Mochamad Apri

Minimizing Parameter and Dynamical Uncertainties in Biological Models


Time : 09.00 – 10.40

Room : Lily

Chair : Dr. Windarto


09.00 – 09.20 Invited Talk 11 Windarto On modified logistic growth model

09.20 – 09.40 4 Siti Laelatul Chasanah, Dipo Aldila and Hengki Tasman

Mathematical Analysis of a Tuberculosis (TB) Transmission

Model With Vaccination in an Age Structured Population

09.40 – 10.00 38 Kemal Adam Roisy and Dipo Aldila

SIR-SI Model for Malaria Disease with Treatment and Vector Control

10.00 – 10.20 40 Puji Andayani, Lisa Sari, Agus Suryanto and Isnani Darti

Mathematical Model of Zika Virus Transmission with Saturated Incidence

Rate

10.20 – 10.40 7 R. Heru Tjahjana and Sutimin The Utilization of Optimal control on the HIV-1 Infection in CD4+ T Cells

with RTI and PI Therapy


Time : 09.00 – 10.40

Room : Asoka

Chair : Dr. Nursanti Anggriani


09.00 – 09.20 Invited Talk 12 Nursanti Anggriani

Dynamical and global sensitivity analysis of dengue mathematical

model considering reinfection with the same serotype.

09.20 – 09.40 3 Dian Setyorini, Bevina D. Handari and Dipo Aldila

Numerical Analysis of The Impact of Loss-Sight and Undetected Cases in

The Spread of TB

09.40 – 10.00 35 Kestrilia Rega Prilianti, Tatas H.P. Brotosudarmo, Syaiful Anam and Agus Suryanto

Performance Comparison of the Convolutional Neural Network Optimizer for Photosynthetic

Pigments Prediction on Plant Digital Image

10.00 – 10.20 5 Ahmad Rizal, Dipo Aldila and Bevina D. Handari

Mathematical Models for The Dynamics of The HIV with

Antiretroviral Treatment Interventions and The Effect of Apoptosis on T-

Cells

10.20 – 10.40 32

Andreas M.M., Ari Juanda, Febi Andika, Hasri Bhakti

Permana, Prama Setia Putra and Nuning Nuraini

Exploration on Virus Transmission using Complex Networks: Pandemic

Flu in Los Angeles


Time : 09.00 – 10.40

Room : Peony

Chair : Dr. Nuning Nuraini


09.00 – 09.20 Invited Talk 13 Nuning Nuraini, Novriana Sumarti and Meta Kallista Having Fun with S-I-R Model

09.20 – 09.40 15 Robiatul Witari Wilda,

Trisilowati Trisilowati and Aruman Imron

Sensitivity and Stability Analysis of SEIR Epidemic Model with

Information

09.40 – 10.00 20 Heni Widayani and Nuning Nuraini

Effect of Host Mobility in Dengue Dynamical Model Inter-two cities

10.00 – 10.20 23 Mia Siti Khumaeroh, Nuning Nuraini and Edy Soewono

A Dynamical Model of ‘Invisible Wall’ in Mosquito Control

10.20 – 10.40 28 Mona Zevika and Edy Soewono On the Risk of Zika Virus Infection for Travelers

PLENARY TALK

Article number : PT01

From In�situ Host�Seeking data tocontinuous malaria modelling

Anna Shcherbacheva1, Amadi Miracle2, Heikki Haario2,⇤

1 University of Helsinki, Finland2Lappeenranta University of Technology. Finland

⇤[email protected]

AbstractIncreasingly complex models have been developed to characterize the transmissiondynamics of malaria. A well�known pitfall in this field is the lack of experimental realdata, that would allow a proper calibration of the model parameters. On the other hand,the multiplicity of malaria transmission factors calls for a realistic modeling approachwhich incorporates various complex factors such as the effect of control measures,socio�economical variables, behavioral impacts of the parasites to the vector and interseasonal variability. We present an approach which combines in-situ data and the keyparameters of continuous epidemiological model for malaria transmission. We stick tothe classical Ross malaria model, but express the model parameters for biting rates andmortality as functions of the coverage of the population with LLINs. This is achievedby agent-based stochastic simulations, initially calibrated with hut-level experimentaldata. Subsequently, the results are generalized for community�level scenarios whileemploying regression analysis to fit response surfaces for the simulated contact andmortality rates. In addition to LLINs, complex phenomena such as change of behaviorof the infected vector and the impact of different household sizes is included in theapproach. The performance of the approach is tested against field data of EntomologicalInoculation Rate values.


1


A Problem in Selecting between HumanMobility and Migration Model in

Dengue Disease TransmissionEdy Soewono

Department of Mathematics, Institut Teknologi Bandung,Bandung, Indonesia


AbstractThe complexity of dengue transmission problem has been understood as a sophisticatedphenomenon that is not fully understood. In reality not all phenomena which arecontributing to the intensity of dengue infection can be accommodated perfectly inexisting mathematical models. Among other sophisticated phenomena that cannot besatisfactorily adopted in the mathematical model is people’s mobility. It is very commonthat a person is infected with dengue in a location far from her/his home. The movementof people may vary from daily travel to offices, temporary visits to other places or evenchanging residences. The main question is how to measure the effect of mobility tothe dengue incidences. For example, with the incoming large number of people fromJakarta to Bandung during weekends, what is the consequences to the dengue incidencein Bandung as well as in Jakarta. We consider here two cases of simplification, migratingpeople from one patch to other patch and mobility of people as part of the daily movementfrom one patch to another and returning to their homes. In general the (global) basicreproduction ratio of a system, if it is possible to construct, is not enough to measure theeffect of mobility on each patch. Instead, the reproduction ratios which represent theendemic threshold in each patch are constructed analytically and analyzed.


2


Chaos Via Torus Destruction inPopulation Biology and Its Implications

for Data AnalysisNico Stollenwerk1,⇤, Maıra Aguiar2, Bob W. Kooi3

1CMAF�CIO, Lisbon University, Portugal2Centre for Mathematics and Applications, Faculty of Sciences and Technology, NOVA

University of Lisbon, Portugal3Free University Amsterdam, The Netherlands


AbstractIn the analysis of relatively simple models for dengue fever epidemiology, describingantibody dependent enhancement ADE and temporary cross�immunity, we encounteredHopf and torus bifurcations and, by increasing parameters slightly further, also theonset of deterministic chaos characterized by positive dominant Lyapunov exponents[1]. Such models describe well the large fluctuations observed in time series of denguefever hospitalization cases. However the models are already high dimensional and anydata analysis is difficult because of the chaotic behaviour and also the high number ofinitial conditions. We therefore search for simpler models in population biology withsimilar dynamical behaviour, one of the simplest originating from ecological models ofRosenzweig�MacArthur (R�MacA) type. The classical R�MacA model shows a Hopfbifurcation which under seasonal forcing turns into a torus bifurcation. By increasingthe forcing further the onset of deterministic chaos was observed and e.g. describedin [2], but lacking a further analysis of the onset of chaos as the tori break off. Viathe analysis of two dimensional dominant Lyapunov exponent plots we revealed thechaotic regions to be inside Arnold tongues of the original tori [3]. This gives a firsthint of further analysis of the original dengue fever models in which the interplay ofdifferent sub�systems can give rise to a similar scenario. Since the original denguemodels are not seasonaly forced, the analysis of the autonomous systems place additionaldifficulties in identifying the interplaying frequencies. The full understanding of thisdynamic scenario helps in the subsequent data analysis of empirical time series of denguefever hospitalization cases, e.g. via iterated filtering, since it turns out that not a singlemodel is describing the large fluctuations of the data but a dynamic scenario [4]. Wewill elaborate on this aspect of data analysis via quite new tools of model comparisonas e.g. given by Bayes factor analysis. And again, the understanding of such models isvital for the understanding of any intervention measure, as e.g. the impact of the newlylicensed dengue fever vaccine, which however turned out to be quite problematic ex-actly because of the subtle interplay between ADE and temporary cross�immunity [5, 6].

Keywords: (Dengue fever and chaos, Lyapunov exponents, Rosenzweig�MacArthurmodel, torus bifurcation, Arnold tongues)


3

References1. Aguiar, M., Stollenwerk, N., & Kooi, B. (2009). Torus bifurcations, isolas and

chaotic attractors in a simple dengue fever model with ADE and temporary crossimmunity. Int. J. Comput. Math., 86, 18671877.

2. Kuznetsov, Y. A. (2004). Elements of Applied Bifurcation Theory. No. 112, AppliedMathematical Sciences ( 3rd ed.). New York: Springer�Verlag.

3. Stollenwerk, N., Fuentes Sommer, P., Kooi, B., Mateus, L., Ghaffari, P., & Aguiar,M. (2017). Hopf and torus bifurcations, torus destruction and chaos in populationbiology. Ecological Complexity, 30, 9199.

4. Stollenwerk, N., Aguiar, M., Ballesteros, S., Boto, J., Kooi, B., & Mateus, L.(2012). Dynamic noise, chaos and parameter estimation in population biology.Interface Focus, 2, 156169.

5. Aguiar, M., Stollenwerk, N., & Halstead, S. (2016). The Impact of the Newly Li-censed Dengue Vaccine in Endemic Countries. Plos Negl. Trop. Diseases, 10(12),e0005179.

6. Aguiar, M. & Stollenwerk, N. (2017). Dengvaxia: age as surrogate for serostatus,Lancet Infect. Dis., published online Dec 21., doi: https://doi.org/10.1016/ S1473-3099(17)30752-1


4


Bioinformatics, Big Data and PrecisionMedicine

Mohammad Asif KhanCentre for Bioinformatics, School of Data Sciences, Perdana University, Malaysia


AbstractThe turn of the 21st century has heralded unprecedented technological advancements inbiomedical research. This has resulted in the high�throughput and highly automatedquantification and digitization of biological data, driving the omics, big data revolutionthat allows for description of the molecular landscape of individuals, with astonishingdepth and breadth. The translation of these advancements to improvement in clinicalcare, especially with respect to precision medicine, however, has been largely limited.Understanding complex diseases and translating the discoveries in a targeted fashionrequire significant cross�disciplinary collaboration. Bioinformatics is a transformativescience that brings together this form of collaboration. Development of sophisticatedbioinformatics tools, powered by Artificial Intelligence, among others, to map geneticvariations to phenotypes accurately are enabling selective treatment approaches, targetingthe root causes of diseases/disorders.


5


Modeling the Implementation ofDengue Vaccine: The History Behindthe Model and Its Impact on Public

Health Practical InterventionMa`ira Aguiar 1,⇤ , Scott B. Halstead2, Nico Stollenwerk3

1Centre for Mathematics and Applications, Faculty of Sciences and Technology, NOVAUniversity of Lisbon, Portugal

2Private consultant, North Bethesda, USA33CMAF�CIO, Lisbon University, Portugal


AbstractDeveloped by Sanofi Pasteur, a tetravalent dengue vaccine, Dengvaxia, was recentlyrecommended by the World Health Organization (WHO) Strategic Advisory Group ofExperts (SAGE) on Immunization, based partially on modeling results, to be used incountries with high dengue endemicity as evidenced by seroprevalence in the targeted agegroup of more than 50% (preferably 70%) [1]. Analyses of clinical trial data demonstratethat individuals who were seronegative (never infected with a dengue virus prior tovaccination) when vaccinated routinely develop non-protective dengue antibodies [2, 3].Surprisingly, despite high rates of overt disease among vaccinated seronegative persons,mathematical models of populations with a seroprevalence of 70% have estimated anoverall reduction of dengue hospitalizations on the order of 10 30% over a period of30 years, with 80% vaccine coverage of 9 year�olds [1, 4]. It should be noted thataccurate predictions in complex systems such as described in [4] can be only made forshort periods of time. A 20�30�year prediction horizon puts in doubt the beneficialresults of vaccine administration [5]. In this talk I will present an age structured modelthat was developed based on the WHO�SAGE recommendation to vaccinate personsage 9�45 years in dengue endemic countries. The model was used to explore theclinical burden of two vaccination strategies: 1) Vaccinate individuals, ages 9�45 years,seropositives and seronegatives, and 2) vaccinate individuals, ages 9�5 years, who aredengue immune only [6]. A sensitivity analysis of the proposed model will be discussed.Our mathematical model finds that significant reduction of hospitalizations can be onlyachieved when vaccine is directed exclusively to seropositive individuals [6]. Whenusing a more recent data set by age and serostatus from the combined CYD14, CYD15,CYD57 trials, as reported in Table 1 in Martinez�Vega et al. [7], we confirm statisticallythe vaccine induced risk in seronegative individuals [8],[9].

Keywords: (Deterministic chaos, Positive Lyapunov exponents, Age structured models,Serostatus, Vaccine efficacy))


6

References1. World Health Organization Strategic Advisory Group of Experts (SAGE) on

Immunization. (2016). Background paper on Dengue Vaccines prepared bythe SAGE working group on dengue vaccines and the WHO secretariat. Re-trieved from http://www.who.int/immunization/sage/meetings/2016/april/presentationsbackgrounddocs/en/.

2. Hadinegoro, S. R., Arredondo�Garcìa, J. L., Capeding, M. R., et al. (2015). Ef-ficacy and long�term safety of a dengue vaccine in regions of endemic disease, N.Engl. J. Med., 373, 11951206.

3. Halstead, S. B. & Russell, P. K. (2016). Protective and immunological behavior ofyellow fever dengue chimeric vaccine. Vaccine, 34 (14), 16431647.

4. Ferguson N, Rodrìguez�Barraquer I, Dorigatti I, et al. (2016). Benefits and risksof the Sanofi�Pasteur dengue vaccine: modeling optimal deployment. Science,353, 10331036.

5. Aguiar, M., Stollenwerk, N., & Halstead, S. B. (2016). The risks behind Dengvaxiarecommendation. The Lancet Infectious Diseases, 16, 882.

6. Aguiar, M., Stollenwerk, N., & Halstead, S.B. (2016). The impact of the newlylicensed dengue vaccine in endemic countries. PLoS Negl. Trop. Dis., 10(12):e0005179.

7. Martìnez�Vega, R. A. et al. (2017). ADE and dengue vaccination. Vaccine, 35,39103912.

8. Aguiar, M. & Stollenwerk, N. (2017). Dengvaxia efficacy dependency on serosta-tus: a closer look at more recent data Clinical Infectious Diseases, Online publica-tion on Oct. 21, 2017. doi: https://doi.org/10.1093/cid/cix882

9. Aguiar, M. and Stollenwerk, N. (2017). Dengvaxia: age as surrogate for serosta-tus, The Lancet Infectious Diseases. Online publication on Dec. 21, 2017. doi:http://dx.doi.org/10.1016/S1473�3099(17)30752-1


7

INVITED TALK


8

Article number : IT01

Global Stability of A Discrete SIREpidemic Model with Saturated

Incidence RateAgus Suryanto

Department of Mathematics Faculty of Mathematics and Natural Sciences, BrawijayaUniversity, Jl. Veteran Malang 65145 INDONESIA


AbstractIn this work a nonstandard finite difference scheme is implemented to discretize a SIRepidemic model with saturated incidence rate. The dynamical properties of the obtaineddiscrete model are then analyzed. It is found analytically that the discrete model preservesall essential properties of the continuous model such as the positivity and boundednessof the solutions as well as the equilibrium points and their stability properties. Thestability analysis here is performed locally via linearization of the discrete system aroundeach equilibrium point and globally using discrete-time analogue of Lyapunov functions.Both local and global asymptotic stability of the equilibria are fully determined thebasic reproduction number (R0) irrespective of the time step size. We conclude that ourdiscretized epidemic model is dynamically consistent with the corresponding continuousmodel. The analytical results are confirmed by numerical simulations.

Keywords: (Discrete epidemic model, Nonstandard finite Difference scheme, Dynami-cally consistent, Global stability, Lyapunov function)


A Comparison of Fuzzy ClusteringApproaches for Gene Expression

Profiling in Advanced Breast Cancerafter Neoadjuvant Chemo-and

Hormone TherapySetia Pramana1,⇤, Syarifah Dewi2, Septelia Inawati Wanandi2, Ramadhan Karsono3

1Center for Computational Statistics Studies, Politeknik Statistika STIS2Department of Biochemistry and Molecular Biology, Faculty of Medicine, Universitas

Indonesia3Department of Oncology Surgery, Dharmais National Cancer Hospital


AbstractNeoadjuvant chemo-and hormone therapy has been widely used for locally advancedbreast cancer patients to reduce tumor size. However, the effect of both neoadjuvanttherapy (NAT) on metastatic breast cancer remains unknown, particularly in associa-tion with apoptotic-pathway. Several studies have been carried out to investigate theexpression of p53�apoptotic pathways genes in advanced breast cancer patients usingstandard approach such as the hierarchical clustering. Although this form of clusteringshows basic cluster patterns, the accuracy of clusters need to be investigated further. Inthis study, we investigate of the gene expression profile in distinguishing breast cancerusing advanced clustering approaches. We collected stage IIIb and IV breast cancertissues from 46 patients before and after neoadjuvant chemo� (5�fluorouracil, anthra-cyclines, cyclophosphamides) and hormone (tamoxifen or aromatase inhibitor) therapy.Patients were treated for 6 months prior to tumor resection. The expression profile ofp53�pathway genes was investigated using Next�Generation Sequencing and TargetedRNA expression p53 panel comprising of 52 genes (TruSeqr, Illumina). Several clus-tering methods, Fuzzy C�Means, Gustafsson Kessel FCM, Ensemble GK FCM methodsare implemented and then compared using cluster validation indexes (Xie Benie, PartitionCoefficient, Modified Partition Coefficient, Classification Entropy, Kwon, Tang, and Sep-aration Indexes). The study reveals alteration of several p53�pathway gene expressionswhich indicate the effectiveness of both chemo- and hormone therapy to suppress tu-mor proliferation and induce apoptosis in advanced breast cancer prior to mammosurgery.

Keywords: (Next generation sequencing, Fuzzy clustering, Breast cancer, Gene expres-sion)


10


From Data to Drug Decisions: HowPrecision Medicine Can Help Solve Real

World ProblemsMaulana Bachtiar

Yong Loo Lin School of Medicine, National University of Singapore (NUS), and the DataAnalytics Lead of the Data Analytics Core at the Medical Sciences Cluster


AbstractData is disrupting the way our society functions. While Go-Jek and Grab show how deepapplication of data analytics can facilitate a more efficient public transportation on theroad, the healthcare industry is also going to benefit from human data utilization. But,real world application of traditional pharmacogenomics is challenging, partly due to thepresence of population differences that are manifested in various levels in the clinics. Asmore data becomes available in healthcare, such as through greater adoption of electronichealth record platform and lower cost of DNA sequencing, analytics would propel a fasteradoption of ’precision medicine’ in the clinics. Here, I will share how data analyticsmethod can be applied in medical translational research, which can potentially lead toa faster adoption of precision medicine in healthcare in both developed and emergingeconomies.


11


Smart Probe for Intracellular Imaging:Lets Tame It!

Samira Husen AlamudiAgency for Science, Technology and Research (A⇤STAR), Singapore

⇤[email protected], samira [email protected]

AbstractFluorescence labelling of an intracellular biomolecule in native environment is a power-ful strategy to achieve in-depth understanding of the biomolecules roles and functions.Besides being nontoxic and specific, desirable labelling probes should be highly cellpermeable without nonspecific interactions with other cellular components. In this talk,I will discuss on the development of predictive model for designing such fluorescenceprobe by utilizing high-throughput screening in combination with cheminformatics.The results provide an efficient strategy for designing cell-permeable probes with nobackground interference. These probes, which are referred to as being tamed in character,provide novel tools for bioimaging applications in living condition.


12


Modelling Commuter Data for Denguein Jakarta

Dipo Aldila1,⇤, Nathania Audia 1, and Prama Setia Putra 2

1Department of Mathematics, Universitas Indonesia1Department of Mathematics, Institut Teknologi Bandung


Abstract

A mathematical model of dengue spread will be discussed in this talk. A commuter ofhuman in Jakarta which describes the daily mobility of human for working and schoolpurposes is included into the model. Mathematical analysis of equilibrium point andtheir local stability were analyzed. Basic reproduction number as the spectral radius ofthe next-generation matrix conducted analytically. For a simple model which involveonly two districts, the basic reproduction number is taken from the maximum of thelocal basic reproduction number for each district. Numerical sensitivity analysis ofbasic reproduction number respect to the mobility parameters is shown to give a betterunderstanding of how mobility might impact the spread of dengue.

Keywords: (dengue, commuter, mobility, equilibrium, basic reproduction number)


13


Analysis of Mathematical Model ofHIV�1 Infection in CD4+T Cells Due

to Cells to Cells Contact withAntiretroviral Treatment

Sutimin⇤, R. Heru Tjahjana, SunarsihDepartment of Mathematics, Diponegoro University, Semarang, Indonesia


AbstractWe modify a mathematical model that captures the spread of HIV�1 infection of CD4+Tcells by taking into account the contact from infected cells to healthy cells, the clearanceof virus by healthy cells, and incorporating antiretroviral treatment. We analyze the modelto describe the dynamics of HIV�1 infection and the effect of antiretroviral treatment inreducing the progression of HIV�1 infection. The basic reproduction number is derivedfrom the next generation matrix of the model, then we analyze the stability of equilibriaof the model. We analyze the stability of free disease equilibrium by using linearization,and the stability of endemic equilibrium by constructing Lyapunov function. If the basicreproduction number less than unity, free disease equilibrium is locally asymptoticallystable, while endemic equilibrium is globally asymptotically stable when the basicreproduction number large than unity. The numerical results show that in the preventingof HIV�1 infection, the treatment of RTI drug may be more effective than that of PI drug.

Keywords: (HIV-1 infection, RTIs, PIs, CD4+T cells)

References1. Chirove, F., S., Sutimin, Soewono, E., Nuraini, N. (2014). Analysis of Combined

Langerhans and CD4+ T Cells HIV Infection. SIAM Journal on Applied Mathe-matics, 74(4), 1174-1193.

2. Srivastava, P. K., Banerjee, M., & Chandra, P. (2009). Modeling in Drug Therapyfor HIV Infection. Journal of Biological Systems, 17(2), 213-223.

3. Sutimin, Chirove, F., Soewono, E., Nuraini, N., & Suromo, L., B. (2017). A modelincorporating combined RTIs and PIs therapy during early HIV�infection. Mathe-matical Biosciences, 285, 102-111.


14


Indonesian Mangroves Extract Library:an Ideal Model towards Integration ofIndonesian Biodiversity Information

SystemKholis Abdurachim Audah1,2

1Academic Research and Community Services2Department of Biomedical Engineering, Swiss German University, Prominence Tower,

Alam Sutera, Tangerang 15143, Banten, Indonesia


AbstractIndonesia is home of approximately 30000 or about 10% of the worlds flowering plantsand other biota both in land and marine with significant figures. This figure is ofinteresting facts regarding Indonesian biodiversity, which is considered as one of themost diverse in the world. The information can be more interesting and meaningful ifdetails about particular biota is also known. Development of Indonesian Extract Libraryis very important as a small step towards the integration of the Indonesian BiodiversityInformation System. The library should include but not limited to name and species,location, chemical composition and usage of a biota such as for foods, biomedicalapplications or other human needs. Additional information such as used methods orpublications would be very useful as reference for further investigation. Among ofmany potential plants, Mangroves are very potential ones to be explored and used asan ideal model to develop an extract library. The library can be then expanded for anyother organisms originated from Indonesian land or water. Implementation of barcodingsystem and integration of all data into a comprehensive information system is necessary.This can be utilized as a window of the Indonesian biodiversity as a whole and can beutilized for different purposes such as drug discovery and other noble causes for thebetterment of human being.

Keywords: (Drug discovery, Extract library, Mangroves, Indonesian biodiversity,Information system)


15


Analysis of Multimodal Data usingFundus Images and Gene Expression

Data to Diagnosis of DiabeticRetinopathy

A. Bustamam⇤, D. Sarwinda, Gianinna Ardaneswari, Titin SiswantiningDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas

Indonesia


AbstractDiabetic Retinopathy is a disease caused by long�term microvascular complications ondiabetes mellitus patients. This research investigates texture feature capabilities fromfundus images and gene expression data to detect diabetic retinopathy (DR). In our pro-posed method, we used two different methods for processing our data. In fundus images,we used improvement of local binary pattern (LBP) with calculation of LBP originalvalue and magnitude value of fundus images. This method is compared with Local LineBinary Pattern (LLBP). In this study, two experiments (DR�Normal, Multiclass) weredesigned for two databases, DIARETDB0 database and STARE. Kernel PCA is choosedas feature selection method, and three classifiers are tested (Naive Bayes, SVM, andKNN). While, we implemented parallel Two-Phase Biclustering for gene expression data.For the first phase, we used parallel K�Means algorithm and the second phase usingCheng�Church Biclustering algorithm. The experimental results show that our proposedmethod has higher accuracy than LLBP, with accuracy of binary classification 100%for DRNormal and AMD-Normal. While, multiclass classification (DRAMD�Normal)achieves an accuracy 80�84%. Another results show that our proposed method givegood performance in running time. These results suggest that our proposed method inthis paper can be useful in a diagnosis aid system for diabetic retinopathy.

Keywords: (Diabetic retinopathy, Fundus images, LBP, Gene expression data, Bicluster-ing, Parallel computing)


16


On Modified Logistic Growth ModelWindarto

Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga


AbstractThe mathematical model of growth has been extensively used to describe the dynamicsof population growth, the spread of a rumor, the dynamics of chemical reactions andartificial neural network techniques. Population growth models can be classified intoempirical growth models (e.g. Weibull model and Morgan-Mercer-Flodin model) anddynamic growth models (growth models derived from a differential equation). Mostdynamic growth models are a modification of logistic growth models, including theRichards model and the Gompertz model. In this talk, we present a new modified logisticgrowth model as an alternative model to describe the growth of a population. We alsocompared the sensitivity of some population growth model due to trimmed data. Wefound that the empirical model more sensitive than the dynamic model.

Keywords: (Growth model, Modified logistic model, Empirical model, Trimmed data )


17


Having Fun with S�I�R ModelNuning Nuraini⇤, Novriana Sumarti, Meta Kallista

Institut Teknologi Bandung, Indonesia

⇤[email protected], [email protected], [email protected]

AbstractFrom K�pop to U.S pop star, from movie series to blockbuster movie, mathematicalmodeling can help asses to describe the hits, prediction and some exciting aspect of thatentertainment phenomena. Using only simple, well-known SIR model, we can havefun with this topic to ask students explore deeper and gain insight to do the researchmore applicable. We also deal with an open data source, define a problem, variables,parameters, and do the modeling cycle. We have a good result that makes us learn thedynamical analysis happily.

Keywords: (SIR model, Data source, Modeling cycle)


18

CONTRIBUTED TALK


19

Article number : 001

Leptospirosis Disease Model: SeasonalVariation of Bacterial Population

Rudianto Artiono⇤, Budi Priyo PrawotoDepartment of Mathematics, Universitas Negeri Surabya


AbstractLeptospirosis is a bacterial disease of worldwide importance. This disease can spreadsporadically not only in the human population but also in the domestic animal population.The disease is transmitted by rats, which act as a reservoir for leptospira bacteria. Itis well-known that high rainfall season can increase the number of human cases ofleptospirosis. The survival rate of bacteria is known to change seasonally, mortality beinglower in rainy season and higher in dry season. The aim of this study was to determineseasonal model of leptospirosis. Compartment model was used as a basis of modelconstruction. Model had been built based on real phenomenon which involved humanpopulation, host animal population, vector animal population and leptospira bacteria.Seasonal effect had been considered in the growth of bacteria life cycle. Model analysishad been done through stability analysis of free endemic equilibrium and endemicequilibrium. Numerical simulation had been explored to figure out the behavior ofseasonal model in the future. Some interpretations relate to the biology phenomenon hadbeen summarized logically based on the model constructed.

Keywords: (Epidemiology, Leptospirosis, Seasonal model, Stability analysis)

References1. Murray, J. D. (1989). Mathematical Biology. Berlin Heidelberg New York:

Springer 1989.

2. Garira, W., Mathebula, D., & Netshikweta, R. (2014). A mathematical modellingframework for linked within-host and between-host dynamics for infections withfree-living pathogens in the environment. Mathematical Biosciences, 256, 58-78.Retrieved October, 2014.

3. Holt, J., Davis, S., & Leirs, H. (2006). A model of Leptopsirosis infection in anAfrican rodent to determine risk to humans: Seasonal fluctuations and the impactof rodent control. Acta Tropica, 99(23),218-225. Retrieved October, 2006.


Modelling The Number of NewPulmonary Tuberculosis Cases withGeographically Weighted Negative

Binomial Regression MethodTsuraya Mumtaz1, Agung Priyo Utomo2

1 Majoring in Statistics, Badan Pusat Statistik, Jakarta2 Majoring in Statistics, Politeknik Statistika STIS, Jakarta

[email protected] , 2 [email protected]

AbstractTuberculosis (TB) is an infectious disease caused by Mycobacterium Tuberculosis.Untill now, TB is still one of the main problems in many countries, especially developingcountries. Indonesia ranked second as the country with the highest TB cases in the worldin 2015. The number of new pulmonary TB cases in Indonesia continually increase byeach year, where most cases were found in Java. This study was conducted to modelthe number of new pulmonary TB cases in Java by considering the spatial aspectsand overdispersion using Geographically Weighted Negative Binomial Regression(GWNBR). As an evaluation, this study also compared the model resulted fromGWNBR with the model generated from other commonly used methods such as negativebinomial regression and Geographically Weighted Poisson Regression (GWPR). Theresult showed that the population density and percentage of healthy homes were notsignificantly influential in each region. While the number of health centers (Puskesmas),the percentage of smokers, the percentage of good PHBS, the percentage of diabetesmellitus, and the percentage of less BMI were significant in some regions only. Ingeneral, GWNBR model was better for modelling the number of new pulmonary TBcases than negative binomial regression and GWPR.

Keywords: (GWNBR, Spatial, Overdispersion, Pulmonary tuberculosis, Java)

References1. Da Silva, A., & Rodrigues, T. (2013). Geographically Weighted Negative Binomial

Regression: Incorporating Overdispersion. New York: Springer.

2. Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). GeographicallyWeighted Regression. Inggris: University of Newcastle.

3. Hilbe, J. (2011). Negative Binomial Regression (2nd ed.). New York: CambridgeUniversity Press.

4. Ramadhan, R. F. (2016). Pemodelan Data Kematian Bayi dengan GeographicallyWeighted Negative Binomial Regression. Media Statistika, 9(2), 95-106.


21


Numerical Analysis of The Impact ofLoss�sight and Undetected Cases in

The Spread of TBDian Setyorini⇤, Bevina D. Handari, Dipo Aldila

Department of Mathematics, Universitas Indonesia, 16424 Depok, Indonesia⇤[email protected], [email protected], [email protected]

AbstractTB disease until now is one of the world’s health problems. Loss-sight and undetectedcases contribute to the high case in the spread of the TB. A deterministic model of TBincluding losssight and undetected cases with quarantine intervention is presented andanalyzed in this talk. We employed a sensitivity analysis on the basic reproductionnumber (R0) and identified the parameters that should be targeted by treatment strategieswith quarantine intervention. Numerical simulations performed under various scenariosbased on sensitivity analysis of R0 will show how significant the role of treatment withquarantine to overcome the spread of TB. The more people infected with TB disease withloss-sight and undetected cases will be faster also the process of dissemination of TBdisease that occurs. If this condition persists, then the effort to be done to overcome thespread of disease will take a long time, and the cost to be spent for the treatment of TBdisease will be greater.

Keywords: (Dynamical system, Tuberculosis, Mathematical model, Quarantine, Basicreproduction number(R0))

References1. Moualeu, D.P., A. Nana Yakam, S. Bowong, & A. Temgoua. (2016). Analysis of

a tuberculosis model with undetected and lost-sight cases. Commun Nonlinear SciNumer Simulat, 41, 48-63.

2. Moualeu, D.P., M. Weiser, R. Ehrig, & P. Deuflhard.( 2013). Optimal Control forTuberculosis model with undetected cases in Cameroon.

3. Mishra, Bimal Kumal, & Jyotika Srivastava. (2014). Matematical model onpulmonary and multidrug-resistant tuberculosis patiens with vaccination. Journalof the Egyptian Matematical Society.

4. A. Safi Mohammad and Abba B. Gumel. (2011). Mathematical analysis of diseasetransmission model with quarantine isolation and an imperfect vaccine. Computerand Mathematics with Application, 61.

5. Diekmann, O., J.A.P Heesterbeek, and M.G Roberts. (2010). The Construction ofnextgeneration matrices for compartemental epidemic models. Journal of the RoyalSociety Interface.


22


Mathematical Analysis of aTuberculosis (TB) Transmission Modelwith Vaccination in an Age Structured

PopulationSiti Laelatul Chasanah ⇤ , Dipo Aldila , Hengki Tasman

Department of Mathematics, Universitas Indonesia, 16424, Depok, Indonesia


AbstractThis study presents a mathematical model of Tuberculosis (TB) transmission consideringBCG vaccination in an age-structured population to simulate the TB dynamic andevaluate the potential impact on active TB of several vaccination strategies. Wedeveloped a deterministic compartmental model where the population was distributedinto seven compartments, i.e., susceptible individuals that can be vaccinated (S1) andcan’t be vaccinated (S2), vaccinated (V ), slow (L) and fast (E) ex posed, infectious(I) and recovery (R). The mathematical model analysis was done by determiningthe equilibrium point of the system, analyze the stability of the equilibrium pointand determine the Basic Reproduction Number (R0). Some numeric interpretationswere given by sensitivity analysis of parameters u1, u2 and ⇠ to R0 and autonomousmodel simulations. Numerical simulations of the model show that to reach a disease-free equilibrium point is not enough by maximizing one of the parameters u1, u2 or⇠. The vaccine is also more effective given to individuals under 30 years than the newborn.

Keywords: (Tuberculosis (TB), Vaccination, Age structured population)

References1. Department of Health and Human Services Victoria. (2015). Management, Control

and Prevention of Tuberculosis. Melbourne Department of Health and HumanServices.

2. Diekmann et al. (2009). The Construction of Next Generation Matrices forCompartmental Epidemic Model. Journal of The Royal Society Interface 7, pp.873-885.

3. E. Soewono and D. Aldila. (2015). A survey of basic reproductive ratios in vector-borne disease transmission modeling. AIP Conf. Proceedings 1651 (1)-7, 12.

4. Legrand, Judith et al. (2008). Modeling the Impact of Tuberculosis ControlStrategies in Highly En- demic Overcrowded Prisons. PloS ONE 3(5): e2100. doi:10.1371/journal.pone.0002100.


23


Mathematical Models for The Dynamicsof The HIV with Antiretroviral

Treatment Interventions and The Effectof Apoptosis on T�Cells

Ahmad Rizal⇤, Dipo Aldila, Bevina D. HandariDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, University

Indonesia, Depok 1624, Indonesia


AbstractThe development of HIV, when evaluated in vivo can be modeled into a system ofordinary differential equations using a deterministic approach. Until now, there is nomedicine to cure HIV infection, but there is a treatment that can slow the progression ofHIV in the body called Antiretroviral Treatment. In this paper, be formed a mathematicalmodel for the dynamics of HIV in the body with the intervention of AntiretroviralTreatment and take into account the influence of Apoptosis on T�cells. The dynamicsystem analysis of the model uses the Routh�Hurwitz criterion and analyzes the BasicReproduction Number (R0) to determine the stability of the infectious free equilibriumpoint and the endemic equilibrium point. Numerical simulations are performed toanalyze the effects of Antiretroviral Treatment intervention and the impact of Apoptosison T�cells in inhibiting HIV progression.

Keywords: ( HIV, Antiretroviral treatment (ART), Apoptosis, Equilibrium point, T�Cells )

References1. i-base. (2016). Introduction to ART.

2. Timilsina, Uddhav et al. (2016). Modulation of apoptosis and viral latency.

3. Shonkwiler, R., W. (2009). Mathematical Biology:An Introduction with maple andmatlab.

4. Rivadeneira, P., S. (2014). Mathematical Modeling of HIV Dynamics After Retro-viral Therapy: A Review.

5. Diekmann, O, J.A.P Heesterbeek, and M.G Roberts. (2010). The Constructionof next-generation matrices for compartemental epidemic models, Journal of theRoyal Society Interface.


24


The Utilization of Optimal control onthe HIV�1 Infection in CD4+ T Cells

with RTI and PI TherapyR. Heru Tjahjana⇤, Sutimin

Departement of Mathematics, Diponegoro University


AbstractThe purpose of this paper is to expose the optimal strategy of controlling HIV�1infection in CD4+ T cells with RTI and PI therapy. The scope of the paper includes amodel of the dynamic system of HIV�1 infection in CD4 cells and a functional costmodel that minimizes the population of free virus and therapeutic costs. From thedynamics system model and cost functional model are designed for optimal control forHIV�1 infection control. In this paper are obtained optimal control for RTI and PItherapies. The conclusions of this paper obtained are as follows, with the optimal controlapproach obtained infectious control strategy that minimizes the population of free virusand the cost of therapy. In other words, optimal control can be used as a good approachin determining infection control strategies that minimizes the population of free virus andthe cost of therapy.

Keywords: (Optimal control, RTI therapy, PI therapy)

References1. Chirove, F., S., Sutimin, Soewono, E., Nuraini, N. (2014). Analysis of Combined

Langerhans and CD4+ T Cells HIV Infection. SIAM Journal on Applied Mathe-matics, 74(4), 1174-1193.

2. Sutimin, Chirove, F., Soewono, E., Nuraini, N., & Suromo, L., B. (2017). A modelincorporating combined RTIs and PIs therapy during early HIV�infection. Mathe-matical Biosciences, 285, 102-111.

3. Sutimin, Nuraini, N., Chirove, F., & Suromo, L.. B. (2017). Modelling MultipleDosing with Drug Holiday in Antiretroviral Treatment on HIV�1 Infection. Jour-nal of Mathematical and Fundamental Sciences, 49(1), 1-20.

4. Srivastava, P. K., Banerjee, M., & Chandra, P. (2009). Modeling in Drug Therapyfor HIV Infection. Journal of Biological Systems, 17(2), 213-223.

5. Elaiw, A. M. (2010). Global properties of a class of HIV models. Nonlinear Anal-ysis: Real World Applications, 11(4), 2253-2263.


25


The Importance of Social InteractionFactors on The Type 2 Diabetes Mellitus

Prognosis ModelR.Ratianingsih⇤, Hajar, A.I.Jaya

Mathematics Study Program of Tadulako University


AbstractThe preview work on diabetes mellitus (DM) model stated that obesity is the crucialphase of DM prognosis that consisted of several phases. The phases are susceptible(SN ), overweight (SO), obesity (O), DM , metabolic syndrome (MS) and chronic (C),a condition indicated by such another coexist disease. This paper reconsiders the phaseof MS not only as a risk factor of DM but also as a trigger factor of it. It means thatthe next phase of DM phase could be SM and the next phase of SM phase could beDM. Comparing to the preview model, the overweight-obesity transition rate ( ) and thesuccesness of positive interaction between O and o S and or N S and between N S and NS , that is , are the important parameters to be considered for the existence of the criticalpoint. The stability of the critical point of the nonlinear system is identified from theJacobian matrix in form of six order factorized characteristic polynomial. The first-orderprovides a negative eigenvalue, while the second-order polynomial gives a discriminantvalue that identify the stability of the critical point. Such positive discriminant leads toa positive eigenvalue that comes to the unstable critical point becomes. When the dis-criminant is negative, the stability identification is extended to the third-order polynomialusing the Routh Hurwitz criteria. Some requirements are needed to justify a stable criticalpoint. The appearance of and parameters as the requirements of a stable critical pointshows the importance of the social interaction in the DM prognosis. Finally, the discus-sion is completed by simulation that represents the dynamic of the DM prognosis process.

Keywords: (E)

References1. Murray, J. D., 1989, Mathematical Biology, Berlin Heidelberg New York: Springer

1989


26


Mathematical Model of the Effect ofBears on the Pacific Salmon Population

in British ColumbiaJane Sahetapy-Engel, Azhary Ramadhanty, Eduardus Axel Wijaya, Dancent Sutanto,

Ambar Winarni and Prama Setia PutraDepartment of Mathematics,

[email protected], [email protected],[email protected], [email protected].,

[email protected], [email protected]

AbstractAn interaction model for the Pacific salmon and bear population in British Columbiais discussed here. The phenomenon is shown during the salmons period of migrationback to their birthplace river at the end of their life. During this returning home, largenumber of bears from the nearby state come and prey on them. This predation of salmonbefore spawning is suspected as the cause of the decline in Salmon production. Here adynamical model involving a specific predator-prey type interaction between Salmon andBears is constructed in the form of a non-autonomous dynamical system, in which thetransition rate from the adult state of salmon to the spawning state is positive only in themonth of migration. A dynamical analysis for stability of the coexistence equilibrium forthe autonomous case is shown and a sensitivity analysis for the non-autonomous case isdone numerically.

Keywords: ( Predator-prey Equilibrium point Stability analysis)

References


27


Real�Time Dengue Forecasting by theMethod of Analogues

Afrina Andriani br Sebayang⇤, Mochamad Apri, Edy SoewonoIndustrial and Financial Mathematics Group, Faculty of Mathematics and natural

Sciences, Institut Teknologi Bandung, Bandung, 40132, Indonesia


AbstractThe lack of preparedness in handling dengue cases is often caused by a deficiency or aninaccuracy in detecting real-time dengue surveillance data. Presently, with the ability toaccess historical data from dengue cases and with appropriate computational method, it ispossible to develop an epidemiological forecasting method. Accurate forecasting methodwould markedly predict potential risk of dengue outbreak and improve the control andprevention of impending or ongoing epidemics. One of the biggest challenges in thisarea is how to generate real-time predictions and to assess the accuracy of the diseaseforecasting result. In this work, an Analogue method which is one of non-parametricforecasting method is proposed to predict the real-time future trend and prevalence forseveral weeks ahead of dengue incidence cases. Moreover, the forecasting accuracy willbe addressed and tracked by calculating the correlation coefficient and root mean squarebetween observed and forecasted data. As for the latter, the result yields long-term futuretrend prediction of dengue cases and estimates the limit of forecastability which providea basic insight for future dengue monitoring and control strategies.

Keywords: (Epidemic forecasting, Error measure, Analogue method, Prediction)

References1. Viboud, C., Boelle, P., Valleron, A. Flahault, A. (2003). Prediction of the Spread of

Influenza Epidemics by the Method of Analogues. American Journal of Epidemi-ology, 158(10), 996�1006.

2. Casdagli, M. (1997). Chaos and deterministic versus stochastic non-linear mod-elling. Epidemiology, 8, 390�395.

3. Flahault, A., Geissbuhler, A., Guessous, I., Guerin, P. J., Bolon, I., Salathe, M.,Escher, E. (2017). Precision global health in the digital age. Swiss Medical Weekly,147.

4. Spreco, A., & Timpka, T. (2016). Algorithms for detecting and predicting influenzaoutbreaks: Metanarrative review of prospective evaluations. BMJ Open, 6.


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Plasmodium Classification on Red BloodCells Image using Multiclass Support

Vector MachinesSoya Febeauty Yama O. P.⇤, Alhadi Bustamam, Zuherman Rustam

Department of Mathematics, FMIPA Universitas Indonesia, Kampus UI Depok, Depok16424, Indonesia


AbstractBioinformatic is one of many aspect which is using classification methods. For example,it is used to determine phase level of a disease. This research will classify the phaseof Plasmodium falciparum parasite which causes malaria. This diseases is spread byan infected female Anopheles mosquito which contains Plasmodium. The result of thisresearch could be use to determine Plasmodium parasite phase in infected peoples redblood cells. The purpose of this research is to discover the success rate of MulticlassSupport Vector Machines method and analyze it in order to predict the parasite phaselevels. The data of this study is image data of red blood cells which was infected by threekinds of Plasmodium falciparum parasite levels. In the process, this study will be usingCanopy as Integration Development Environtments of phyton programming language.From 112 trials, the highest number of accuracy is 87.5% for Multiclass Support VectorMachines one vs rest and one vs all methods which used the 4�fold cross validation withC=1 as parameter for both linear and RBF kernel with � = 0.0001.

Keywords: (Malaria, Plasmodium falciparum, Classification, Multiclass support vectormachines.)

References1. Hsu, C., & Lin, C. (2002). A comparison of methods for multiclass support vector

machines. IEEE Transactions on Neural Networks, 13(2), 415�425.

2. Gatc, J., Maspiyanti, F., Sarwinda, D., & Arymurthy, A. M. (2013). Plasmodiumparasite detection on Red Blood Cell image for the diagnosis of malaria using dou-ble thresholding. 2013 International Conference on Advanced Computer Scienceand Information Systems (ICACSIS).

3. Maspiyanti, F., Nursari, S. R., Murtako, A., & Gatc, J. (2016). Plasmodium fal-ciparum stages classification on red blood cell image using region property. 20161st International Conference on Information Technology, Information Systems andElectrical Engineering (ICITISEE).


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A Stage�structure Predator�preyModel with Ratio�dependent

Functional Response and Anti-predatorAdina Apriyani, Isnani Darti ⇤, Agus Suryanto

University of Brawijaya

[email protected], ⇤ [email protected], [email protected]

AbstractThis paper discusses a stage-structure predator-prey model with ratio-dependent func-tional response. The proposed mathematical model is a system of three nonlinearordinary differential equations that describe the interactions between prey population,juvenile predator, and adult predator. It is assumed that only adult predators attackand consume the prey and have the ability to reproduce. Here, we also consider ananti-predator defense effects where prey can attack juvenile predator. However, it isalso assume that adult predators help when juvenile predators are attacked by prey. Theproposed model is analyzed dynamically, which includes the existence and local stabilityof equilibrium points. There are two equilibria, namely extinction of predator and theinterior equilibrium point. The extinction of predator always exists and it is conditionallyasymptotically stable. If the interior equilibrium exists, then it is asymptotically stable.Numerical solutions are carried out to illustrate the theoretical results.

Keywords: (Predator�prey model, Stage structure, Ratio-dependent response function,Anti-predator, Stability analysis )


30


Leslie�Gower Predator�Prey Modelwith Stage�Structure,

Beddington�DeAngelis FunctionalResponse, and Anti�Predator Behavior

Umu Salamah, Agus Suryanto⇤, Wuryansari Muharini KusumawinahyuUniversitas Brawijaya

[email protected], ⇤ [email protected], [email protected]

AbstractIn this paper, we concern with a Leslie-Gower predator-prey model with stage-structureon predator using the Beddington-DeAngelis functional response. The predator popu-lation is divided into two subpopulations, namely juvenile predator and adult predator.It is assumed that only adult predator which has ability to attack prey and to reproduce.Moreover, anti-predator behavior is also considered in this model, which is representedby the possibility of juvenile predator to be attacked by prey. Dynamical analysison the model, including determination of equilibrium points, the existing condition,and the local stability of equilibrium point is performed. There are four equilibriumpoints, namely the extinction of all populations point, the extinction of prey point,the extinction of predator point, and the interior equilibrium point. The extinction ofall populations point and the extinction of prey point always exist, while the predatorextinction point and the interior point exist under some certain conditions. The extinctionof all populations point is always unstable, while the other three equilibrium pointsare conditionally asymptotically stable. Some numerical simulations are performed tosupport the analytical results.

Keywords: ( Predator�prey model, Stage�structure, Beddington�DeAngelis functionalresponse, Anti�predator, Dynamical analysis)


31


Sensitivity and Stability Analysis ofSEIR Epidemic Model with

Information.Robiatul Witari Wilda, Trisilowati⇤, Aruman Imron

University of Brawijaya

[email protected], ⇤[email protected], [email protected]

AbstractIn this paper, the construction and analysis of SEIR epidemic model with informationare discussed. This model contains information about how to prevent the spread ofinfectious diseases which is transmitted by infected individuals to susceptible individuals.Furthermore, the dynamical analysis of the model which includes determination ofequilibrium points terms of existence, stability analysis of the equilibrium points andsensitivity analysis are observed. Local stability of the equilibrium point is determinedby linearizing the system around the equilibrium point and checking for the eigen valuesign of Jacobi matrix at each equilibrium point. Sensitivity analysis is performed byusing sensitivity index to measure the relative change of R0 on each parameter. Based onanalysis result, there are two equilibrium points namely disease free-equilibrium pointand endemic equlibrium points. The disease free-equilibrium point always exists and it islocally asymptotically stable if R0 < 1. Moreover, the endemic equilibrium points existand are locally asymptotically stable under certain conditions. From sensitivity analysis,it is found that disease transmission rate, recruitment rate and number of contacts rate ofinfected are the most sensitive parameters. Finally, numerical simulation is conducted tosupport the analysis result.

Keywords: (Sensitivity analysis, Stability analysis, SEIR epidemic, Information)


32


Evolutionary Dynamic of InsecticidesResistance in two�locus of Anopheles

MosquitoesDani Suandi⇤, Edy Soewono, Kuntjoro Adji Sidarto

Department of Mathematics, Institut Teknologi Bandung


AbstractThe use of insecticides in various countries has long been done in malaria vectorcontrol. Unfortunately, continuous usage has been shown to reduce the effectivenessof insecticides, which is an indication of resistance. Consequently, the managementof resistance needs to be improved such that the insecticides can be used effectively.Improvement is done by rotating different types of insecticides with different target sites,which is known as rotational techniques. However, irregular rotation techniques can alsocause double resistance problem. In this paper, a mathematical model that describesthe dynamic evolution of insecticide resistance is constructed based on different targetinsecticide sites. Existence and stability analysis is conducted to understand the factorsthat can accelerate resistance. Sensitivity analysis is also carried out to investigate theparameters that play essential roles in the evolutionary dynamic of insecticide resistance.Furthermore, numerical simulations are performed to show the effectiveness of rotationaltechniques in decreasing of the resistant mosquito population.

Keywords: (Evolutionary dynamic, Two-locus, Insecticides resistance, Existence andstability)

References1. Diaz, H. et al. (2011). A model for the control of malaria using genetically modified

vectors. Journal of Theoretical Biology, 276(1), 57�66.

2. Hargreaves, K. et al. (2000). Anopheles funestus resistant to pyrethroid insecticidesin South Africa. Medical and Veterinary Entomology, 14(2), 181�189.

3. Li, J., (2011). Modelling of transgenic mosquitoes and impact on malaria transmis-sion. Journal of Biological Dynamics, 5(5), 474�494.

4. Marrelli, M.T., Li, C., Rasgon, J. L., & Jacobs�Lorena, M. (2007). Trans-genic malaria�resistant mosquitoes have a fitness advantage when feeding onplasmodium�infected blood. Proceedings of the National Academy of Sciencesof the United States of America, 104(13), 5580�5583.

5. Takken, W. & Knols, B.G.J. (2009). Malaria vector control: current and futurestrategies. Trends in Parasitology, 25(3), 101�104.


33


A Biclustering Procedure Using BicBinAlgorithm for HIV�1 Human Protein

Interaction Database in NCBIPatuan Pangihutan Tampubolon⇤, Alhadi Bustamam

Mathematics Department, FMIPA, Universitas Indonesia, Kampus UI Depok, 16424,Indonesia


AbstractThe objective of establishing the HIV�1 Human Interaction Database in the NCBI is thatto encourage the scientists to produce more publications. The database consists of twotypes of interactions that are collated from published reports�protein interactions andreplication interactions. Biclustering is one of the data mining technique that may obtaininsight from that database. This technique finds clusters by inspecting both rows andcolumns sets simultaneously. The BicBin algorithm is one of the biclustering method toa binary matrix. Therefore, it requires a systematic procedure to make biclusters from thedatabase using this algorithm. We observe the database and select the HIV�1 proteins,the human proteins, and the interaction keywords. The interaction keywords are derivedinto three classes: regulating, regulated by, and bidirectional. The procedure consists ofseveral steps. The first step is modeling the database into the bipartite graph. The secondstep is making a matrix which entry 1, 1, and X represent the regulating, the regulated by,and the bidirectional interactions respectively. The entry 1 and then become the positiveadjacency matrix and the entry 1 and become the negative adjacency matrix. The laststep is inputting both of the binary matrix into the BicBin program

Keywords: (Protein Interactions, HIV�1, NCBI, Biclustering, BicBin)

References1. Bustamam, A., et. al. (2009). An efficient parallel implementation of markov

clustering algorithm for large-scale protein-protein interaction networks that usesMPI. 5th IMT�GT international conference on mathematics, statistics and theirapplications (ICMSA).

2. Fu, W., et al. (2009). Human immunodeficiency virus type 1, humanprotein interaction database at NCBI. Nucleic Acids Research, 37(Database).doi:10.1093/nar/gkn708

3. Mukhopadhyay, A., Ray, S., & Maulik, U. (2014). Incorporating the type and di-rection information in predicting novel regulatory interactions between HIV�1 andhuman proteins using a biclustering approach. BMC Bioinformatics, 15(1), 26.


34

4. Permata, T. S., & Bustamam, A. (2015). Clustering protein-protein interaction net-work of TP53 tumor suppressor protein using Markov clustering algorithm. 2015International Conference on Advanced Computer Science and Information Systems(ICACSIS).

5. Uitert, M. V., Meuleman, W., & Wessels, L. (2008). Biclustering Sparse Bi-nary Genomic Data. Jounal of Computational Biology, 15(10),1329�1345.doi:10.1089/cmb.2008.0066.


35


Implementation of Factor Analysis forBicluster Acquisition: Sparseness

Projection (FABIAS) on Microarray ofAlzheimers Gene Expression Data

Theresia B. P. Wutun⇤, Alhadi Bustamam, Titin SiswantiningDepartment of Mathematics, University of Indonesia, Depok, Indonesia


AbstractAlzheimers is a chronic neurodegenerative disease that usually worsens over time,progressively destroys memory and other important mental functions. The numberof people with Alzheimers is increased over these years. Treatment can help but thiscondition has no cure. Worldwide, approximately 44 millions people have Alzheimers,with care cost that is up to hundreds of billions every year. To face this alarming problem,we propose an implementation of Factor Analysis for Bicluster Acquisition : SparsenessProjection (FABIAS) to discover hidden patterns from microarray of Alzheimers geneexpression data which include 54675 genes dan 161 samples. The development ofmicroarray tehcnology is used in data store of disease genetic expression. Usually, geneexpression data is arranged in a data matrix, where gene corresponds to one row andeach condition to one column. This research proposed FABIAS as one of biclusteringmethod that is useful to discover some useful pattern or information from the data. Fromthe experimental results, there are five, fifteen and fifty biclusters formed by Alzheimersgene expression data.

Keywords: (FABIA, FABIAS, bicluster, microarray, Alzheimer)

References1. Hochreiter, S. et al. (2010) FABIA: factor analysis for bicluster acquisition. Bioin-

formatics, 26, 1520�1527.

2. Gao, C., Mcdowell, I. C., Zhao, S., Brown, C. D., & Engelhardt, B. E. (2016)Context Spesific and Differential Gene Co�expression Networks via Bayesian Bi-clustering. PlOS Computational Biology 12(7).doi:10.1371/journal.pcbi.1004791

3. Cheng, Y., Church, G. (2000) Biclustering of expression data. Proceedings. EighthInt. Conf. On Intelligent Systems for Molecular Biology (ISMB00), 93�103.


36


Dynamical Analysis of a Tumor GrowthModel Involving Interferon Gamma

I.J.T.R.Tamsih, Trisilowati⇤, U. HabibahMathematics department, Faculty of Natural Science, University of Brawijaya, Indonesia


AbstractA tumor is cells that grow uncontrollably and become malignant, meanwhile our immunesystem turns out to have inhibitory factors in preventing the tumor development. Thispaper aims to construct and analyze a mathematical model of tumor and its interactionwith some important immune system such as macrophages, activated CD8+ cytotoxicT-lymphocites(CTLs), and the immuno-stimulatory cytokine nnterferon gamma using asystem of four coupled ordinary differential equations. It describes the effect of interferongamma which activates macrophages in tumor decay process. The response of threedifferent levels of macrophages strength are also investigated. Furthermore, dynamicalanalysis is conducted to investigate the existence and the stability of equilibrium points.Regarding to the result, the tumor free equilibrium point always exists and the interiorequilibrium points exist if it satisfies cardans condition. The equilibrium points are stableunder some circumstances. By using some estimated parameters from the literature, wepresent the numerical simulations which confirm to the analysis result.

Keywords: (Dynamical analysis, Interferon gamma, Macrophages, Tumor cells)

References1. Ansarizadeh, F., Singh,M., & Richards, D. (2017).Modelling of tumor cells

regression in response to chemotherapeutic treatment. Applied Mathematica Mod-elling, 48,96�112

2. Banerjee, S., Khajanchi, S., & Chaudhuri, S. (2015). A Mathematical Model toElucidate Brain Tumor Abrogation by Immunotherapy with T11 Target Structure.Plos One, 10(5). doi:10.1371/journal.pone.0123611

3. Boyce, W. E., R. C. Diprima. (2012). Elementary differential equation and bound-ary value problem (10th ed.) New York: John Wiley and Sons, Inc.

4. Pillis, L. D., & Radunskaya, A. (2003). The dynamics of an optimally controlledtumor model: A case study. Mathematical and Computer Modelling, 37(11),1221�1244.


37


Effect of Host Mobility in DengueDynamical Model Inter�two cities

Heni Widayani⇤, Nuning NuraniDepartment of Mathematics, Institut Teknologi Bandung


AbstractTransmission of dengue disease has long been known as a complex phenomenon asindicated by unsuccessful prevention and control of dengue in many countries. Thiscomplication of transmission is caused among others by biological, climatological andhuman factors. The main problems with the human factor are mainly due to populationmobility that is not easily modeled. In this study a simple model for analyzing the effectof human movement between two patches is constructed in the form of SIR�SI type withcontrol terms in mosquito population. The mobilities of human are represented as linearterms with constant rates. The basic reproductive ratio and condition for coexistenceequilibrium are obtained. Relation between mobility rates, control terms and reductionof the basic reproductive ratio is shown analytically. Interpretation for special cases areshown and the corresponding numerical simulation are presented.

Keywords: (Dengue, Mobility, Inter-two cities, Basic reproductive number)

References1. World Health Organization (2009). Dengue: Guidelines for diagno-

sis, treatment, prevention and control. New Edition. Retrieved June5, 2013, from http://whqlibdoc.who.int/publications/2009/9789241547871_eng.pdf.

2. Sutherst, R.W. (2004). Global change and human vulnerability to vector�bornedisease. Clinical Microbiology Review, 17(1), 136�173.

3. Gubler, D.J. (1998). Dengue and Dengue Hemorrhagic Fever. Clinical Microbiol-ogy Review, 11(3),480�496.

4. Wilder, S. A.& Gubler, D. J. Geographic expansion of dengue: the impactof international travel. Medical Clinics of North America, 92(6), 1377�1390.doi:10.1016/j.mcna.2008.07.002

5. Cosner, C., Beier, J. C., Cantrell, R. S., Impoinvil, D., Kapitanski, L., Potts, M. D.,Troyo, A., Ruan, S. (2009). The Effects of human movement on the persistence ofvector-borne diseases. Journal of Theoretical Biology, 258, 550�560.


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http://whqlibdoc.who.int/publications/2009/9789241547871_eng.pdf

http://whqlibdoc.who.int/publications/2009/9789241547871_eng.pdf


Finding Correlated Bicluster from GeneExpression Data of Alzheimer Disease

Using FABIA Biclustering MethodNuning Setyaningrum⇤, Alhadi Bustamam, Titin Siswantining

Department of Mathematics, University of Indonesia, Depok, Indonesia


AbstractAlzheimers disease (AD) is a progressive, chronic neuro-degenerative interference ofthe human brain and the most common cause of dementia that causes problems withmemory, thinking and behavior. Alzheimer’s disease data are gene expression foundwith microarray technique. The purpose of this research is to simultaneously find strongcorrelation bicluster among genes and samples gene expression data of AD available”Affymetrix Human Genome U133 Plus 2.0 Array” with 74 samples normal and 87samples are affected AD in six different brain regions and each sample consisting of54675 genes with an average age of ”79.8 ± 9.1” year. We apply the biclustering method,FABIA (Factor Analysis For Bicluster Acquisition) is a multiplicative biclustering modelthat assumes realistic non�Gaussian signal distributions with heavy tails. The FABIAmodel contains the product of Laplacian variables which is distributed by the Besselfunction. FABIA utilizes well-understood model selection techniques like variationalapproaches and applies the Bayesian framework. The generative framework FABIAto determine the information content of each bicluster that having a high correlationbetween the genes and the samples, so the proposed method has great potential in thefuture of medical research.

Keywords: (Alzheimer, Biclustering, FABIA, Microarray)

References1. Gao, C., McDowell, I. C., Zhao, S., Brown, C. D., Engelhardt, B. E. (2016). Con-

text Specific and Differential Gene Co-expression Networks via Bayesian Biclus-tering. PLOS Computational Biology.

2. Hochreiter, S., Bodenhofer, U., Heusel, M., Mayr, A. (2010). FABIA: Factor Anal-ysis for Bicluster Acquisition. Oxford University Press.

3. Ray, S., Hossain, S. M., Khatun, L., & Mukhopadhyay, A. (2017). A Comprehen-sive Analysis On Preservation Of Gene Co-Expression During Alzheimers DiseaseProgression. BMC Bioinformatics, 18,579


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Biclustering Protein Interactionsbetween HIV�1 Protein and HumanProtein Using LCM�MBS Algorithm

Olivia Swasti⇤, Alhadi BustamamDepartment of Mathematics, University of Indonesia, Depok, 16424, Indonesia


AbstractSome of protein interactions are still unidentified. Thus, many research about proteininteractions had been held. HIV�1 is a dangerous virus that has no medicine yet. Theresearch about HIV�1 proteins and human proteins interactions leads into insight ofdrug target prediction. Biclustering technique is the beginning step before the predictionstep. Biclustering is the process to cluster dataset through two perspectives. Theresult of biclustering can be applied to predict of unidentified protein interactions.Currently, this technique is more efficiently and effectively than experimental technique.The LCM�MBS is one of the biclustering algorithms to find biclusters from proteininteractions dataset. This algorithm uses graph theory as the basic to obtain the maximalbiclique. The algorithm can represent as enumeration tree. Every subtrees result thebicliques which are the biclusters. This algorithm performs quickly and efficiently in theterm of memory consumptions. In this research, we apply the LCM�MBS algorithm for13711 types of interactions between HIV�1 proteins and human proteins. We find 850biclusters which the maximal bicluster has a size of 4 rows and 204 columns.

Keywords: (Protein interaction, Maximal biclique subgraphs, LCM�MBS algorithm)

References1. Bustamam, A., et. al. (2009). An efficient parallel implementation of markov

clustering algorithm for large-scale protein-protein interaction networks that usesMPI. 5th IMT�GT international conference on mathematics, statistics and theirapplications (ICMSA).

2. Li, J., Liu, G., Li, H., & Wong, L. (2007). Maximal Biclique Subgraphs and ClosedPattern Pairs of the Adjacency Matrix: A One-to-One Correspondence and MiningAlgorithms. IEEE Computer Society, 19(12).

3. Mukhopadhyay, A., Ray, S., & Maulik, U. (2014). Incorporating the type and di-rection information in predicting novel regulatory interactions between HIV�1 andhuman proteins using a biclustering approach. BMC Bioinformatics, 15(1), 26.


40


A Dynamical Model of Invisible Wall inMosquito Control

Mia Siti Khumaeroh ⇤, Nuning Nuraini, Edy SoewonoInstitute Teknologi Bandung, Indonesia


AbstractBasically, mosquitoes have the opportunity to choose their blood meal from the availablehost in nature such as mammals, birds, reptiles, amphibians, fish as well as humans. Inthe blood-seeking process, the environmental conditions such as host availability andhost abundance may form the characteristic in the mosquito to choose a particular hostas compared to another host (preferences). The fact that some mosquitoes are the mainvector causing various diseases in humans, has lead to investigate the importance ofmosquitoes control by strategically changing their blood meal preference from humans toanother host. Here we construct a model of preference alteration in mosquito involvinglarva, mosquito (anthropophilic, opportunistic, and zoophilic), human, and animalpopulations, using the control mechanism of repellent clothing usage and fumigationeffect. The dynamical analysis and global sensitivity are analyzed to determine thedominant factor in mosquitoes preference alteration. Analysis result shows that repellentclothing usage increases the number of mosquitoes with zoophilic characteristic (animalsas their blood resources preference), while the fumigation effect becomes the dominantfactor that reduces the mosquito populations as a whole.

Keywords: (Mosquito preference, Invisible wall, Repellent, Anthropophilic, Opportunis-tic, Zoophilic )


41


A Deterministic Model for InfluenzaTransmission of Two Strains withAntibody Dependent Enhancement

(ADE)Hilda Fahlena⇤, Edy Soewono, Nuning Nuraini

Group of Industrial and Financial Mathematics, Faculty of Mathematics and NaturalSciences, Institut Teknologi Bandung, Bandung, Indonesia


AbstractThe emergence of new strains of the Ribonucleic acid (RNA) virus is still an importantissue in the spread of influenza disease. The ability of RNA virus to mutate causes theimmune system not to work properly. When the body is infected by a strain, immunememory cells will save the information about this strain. Memory cells will take actionwhen the same strain strikes again so that the individual person is not re-infected. Insecondary infection with different strains, memory cells can not necessarily function andthe immune system may give wrong responses. This erroneous mechanism of response iscalled antibody�dependent enhancement (ADE). This ADE process results in a personwho is infected with two different strains known as co�infection. The co-infectionprocess will cause the virus to mutate and followed with the appearance of new strains.A SIRS (Susceptible�Infected�Recovered�Susceptible) model is constructed here todescribe two�strain influenza transmission. Model analysis is conducted covering thecondition of existence of coexistence equilibrium and its stability. A special case ofco-infection is discussed thoroughly in which the two strains have the same characteristic.Parameter estimation is done with the use of incidence data for numerical simulation.

Keywords: (SIR model, Strain, Antibody dependent enhancement)

References1. Trifonov, V., Khiabanian, H. & Rabadan, R. (2009). Geographic dependence,

surveillance, and originz of the 2009 Influenza A (H1N1). Virus New EnglandJournal of Medicine, 361, 115�119.

2. Aldila, D., Nuraini, N. & Soewono, E. (2014). Optimal control problem in prevent-ing of swine flu disease transmission. Applied Mathematical Sciences, 8, 69�72.

3. Boianelli, A., Nguyen, V. K., Ebensen, T., Schulze, K., Wilk, E., Sharma, N.,Slegemann�Koniszewski, S., Bruder, D., Toapantan, F. R., Guzman, C. A.,Meyer�Herman, M. & Hernandez�Vargaz, E. A. (2015). Modeling influenza virusinfection: a roadmap for influenza research, Viruses, 7, 5274�5304.


42

4. Kermack, W. O. & McKendrick, A. G. (1927) , A contribution to the mathematicaltheory of epidemics, Proceedings Royal Society London, 115, 700�721.

5. Palese, P. & Young, J.F. (1982). Variation of influenza A, B, and C viruses, ScienceJournal, 215, 1468�1474.


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POLS Algorithm to Find a LocalOptimum Bicluster on Interactions

between HIV-1 and Human ProteinsTesdiq Prigel Kaloka⇤, Alhadi Bustamam

Department of Mathematics, Faculty of Mathematics and Sciences, UniversitasIndonesia, Depok, 16424


AbstractProtein is an important part of organism. Proteins must interact with other proteins toperform its functions properly. One of the interactions between proteins is the interactionsbetween HIV�1 proteins and human proteins. Although HIV�1 and human proteinsinteract, we need to do depth analysis because some of HIV�1 proteins are not interactwith human proteins. Bicluster is the method which used to observe this interaction.Bicluster can groups interactions by rows and columns, so we can analyze it easier. Thelocal search framework based on pairs operation algorithm or called POLS algorithm.POLS algorithm is one of many algorithms to find a bicluster, it us a balanced bicliqueapproach. The algorithm is good for binary data, because the initial step of the algorithmis to find optimum local value. The purpose of finding optimum local is to make surewhether a bicluster can be found or not. In this paper, we use POLS algorithm to findoptimum local on data interactions between HIV�1 proteins and human proteins. Wedivided the data into two types. The first data is HIV positive and the second is HIVnegative. In HIV positive, the optimum local of the interactions are asp, envelope surfaceglycoprotein gp120, BECN1, and IFNG. In HIV negative, we found the optimum local ofthe interactions are envelope surface glycoprotein gp120, envelope surface glycoproteingp160 precursor, ICAM1, and ICAM3.

Keywords: (PPI, Bicluster, POLS Algorithm)

References1. Mukhopadhyay, A., Ray, S., & Maulik, U. (2014). Incorporating the type and di-

rection information in predicting novel regulatory interactions between HIV�1 andhuman proteins using a biclustering approach. BMC Bioinformatics, 15(1), 26.

2. Permata, T. S., & Bustamam, A. (2015). Clustering protein-protein interaction net-work of TP53 tumor suppressor protein using Markov clustering algorithm. 2015International Conference on Advanced Computer Science and Information Systems(ICACSIS).

3. Tastan, O., Qi, Y., Carbonell, J. G., & Klein-Seetharaman, J. (2009). Predictionof interactions between HIV�1 and human proteins by information integration.Pacific Symposium on Biocomputing, 516. NIH Public Access.


44

4. Wang Y., Cai S., & Yin M. (2018). New heuristic approaches for maximum bal-anced biclique problem. Information Sciences, 432, 362�375.


45


A Competition between Javan Rhinos(Rhinoceros Sondaicus) and Javan Bulls(Bos Javanicus) Model with Allee effect

Respati Mentari⇤, Eric HarjantoDepartment of Mathematics,


AbstractAllee effects on population growth are quite common for some spieses in nature. Thiseffect reduces the rate of population growth when the when the population density islow. In this research, we consider a competition between Javan Rhinos (RhinocerosSondaicus) and Javan Bulls (Bos Javanicus) model. The phenomenon is shown in UjungKulon National Park in which the population of Rhinos did not increase for severaldecades. The Allee effect on this model occurs at the rate of Javan Rhino growth causedby inbreeding and sex-ration fluctuations. This model has five equilibrium points withpossible coexistences. Dynamical analysis such as calculation of equilibrium points, con-dition of equilibrium existence and stability analysis of equilibria are shown analytically.Sensitivity analysis and biological interpretation for coexistence are thoroughly discussed.

Keywords: (Allee effects, Competition model, Rhinoceros Sondaicus, Bos Javanicus,Ujung Kulon National Park )


46


Gene Co�expression Network ofAlzheimers Gene Expression

N.A. Wibawa⇤, Alhadi Bustamam, Titin SiswantiningDepartment of Mathematics, University of Indonesia, Depok, Indonesia


AbstractAlzheimers is a dangerous disease that causes dementia. 60% � 70% cases of dementiaare caused by this disease. Recovering gene co-expression network from Alzheimersgene expression data is essential to understand the information about Alzheimers.In this research, we use biclustering method to identify the latent structure among54675 genes and 161 samples of Alzheimers gene expression data. BicMix is a newbiclustering method to find gene expression network. This method has implementedon breast cancer, GTEx, tissue specific data. This method use Bayesian frameworkand models the data as result of multiplication of two sparse matrices, that are loadingand factor matrix. The value of these matrices represent whether or not a gene or acondition included in a bicluster. Three Parameter Beta (TPB) distribution is used toinduce the sparsity of these matrices. Caused by the largeness of gene expression datamatrices that we process, this method use variational expectation maximization (VEM)to obtain all the parameters. Getting all the parameters means that we get the biclusters.Once we get the biclusters, the result can be used to build the gene co-expression network.

Keywords: (Alzheimer, Bicluster, BicMix, Gene expression)

References1. Gao, C., McDowell, I. C., Zhao, S., Brown, C. D., Engelhardt, B. E. 2016. Context

Specific and Differential Gene Co-expression Networks via Bayesian Biclustering.PLOS Computational Biology.

2. Ray, S., Hossain, S. M., Khatun, L., & Mukhopadhyay, A. (2017). A Comprehen-sive Analysis On Preservation Of Gene Co-Expression During Alzheimers DiseaseProgression. BMC Bioinformatics, 18,579

3. Alzheimers Gene Expression data: Alzheimers disease and normal agedbrain. (2003). https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE5281

4. World Health Organization. (2012).Dementia: A public health priority.


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https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE5281

https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE5281


On The Risk of Zika Virus Infection forTravelers

Mona Zevika⇤, Edy SoewonoDepartment of Mathematics, Institut Teknologi Bandung


AbstractIt has been reported that the spread of Zika disease from an endemic country to othercountries was originally distributed by tourists who were traveling and got infected inthe endemic area and returned home with the Zika viruses (ZIKV). The potential threatof the disease from the returning tourists with the ZIKV infection has forced the healthdepartment to find proper precaution to avoid the wide spread of the disease. Here, amathematical model constructed of SIR-SI type with mobility of people from one patch toan endemic patch is constructed. The force of infection is determined by considering themosquito bite parameter and possibly obtaining the Zika virus from infected mosquitoes.Estimation of the risk of travelers to a Zika endemic patch is done by involving the forceof infection or incidensity rate, arrival time, and duration of stay in endemic areas.

Keywords: (Zika, Risk estimates, Force infection, Travelers.)

References1. Massad, E., Rocklov, J., & Wilder-Smith, A. (2013). Dengue infections in non-

immune travellers to Thailand. Epidemiology and Infection, 141, 412�417.

2. Massad, E., Tan, S., Khan, K., & Wilder�Smith, A. (2016). Estimated Zika virusimportations to Europe by travellers from Brazil. Global Health Action, 9, 31669.

3. Lopez, L. F., Amaku, M., Coutinho, F. A., Quam, M., Burattini, M. N., Struchiner,C. J., Wilder-Smith, A., & Massad, E. (2016). Modeling Importations and Exporta-tions of Infectious Diseases via Travelers. Bulletin of Mathematical Biology, 78(2),185�209.

4. Burattini, M. N., Chen, M., Chow, A., Massad, E, et al. (2008). Modelling thecontrol strategies against dengue in Singapore. Epidemiology and Infection, 136,309�319


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MARS and Bagging MARS in StrokeRia Dhea Layla Nur Karisma ⇤, Sri HariniJalan Gajayana 50 Malang, Jawa Timur


AbstractIn 2010, World Health Organization (WHO) predicted cardiovascular cases caused ofdeath amount of 73% total of a disorder of heart function in human. Stroke cause bydisorganized blood circulation in human brain that increase of death in Estonia. Basedon WHO data, Stroke suffered people that has age between 0 and 64 years old. Thelimitation of research is Ischemic and Hemorrhagic patients which are groups of Strokein Medicum Clinic, Tallinn, Estonia. The aim in the research is to classify modifiedrisk factors of Ischemic and Hemorrhagic whom are alcohol consumption, smokers,physical activity habit, body mass index (BMI), diet habit, and weight. Then, it appliedboth Multivariate Regression Spline (MARS) and Bagging MARS. Both are MachineLearning methods to overcome missing value and to increase accuracy. As result, theclassification modified risks factor of Ischemic and Hemorrhagic patient using MARSand Bagging MARS are alcohol consumption, diet habit, smokers, physical activity, andBMI. Based on APER value (Apparently Error) both MARS and Bagging MARS havesimilar value that is 93,65% and 94,73%. In addition, MARS method is more stabilizedmodel than Bagging MARS in the research.

Keywords: (Stroke, Ischemic, Hemorrhagic, Machine learning, MARS, Bagging MARS)

References1. Breiman, L. (1996). Bagging predictors. Machine Learning, 24, 123�140.

2. Bhlmann, P., & Yu, B. (2002). Analyzing bagging. The Annals of Statistics, 30(4),927�961.

3. Friedman, JH. (1991). Multivariate Adaptive Regression Spline (With Discussion).California: Stanford University.

4. WHO (World Health Organization). (2001). Estonian Health Highlights. RetrievedMarch 15, 2017, from http://www.euro.who.int/__data/assets/pdf_file/0008/130040/E74339.pdf

5. World Health Organization. (2014). Modified and Unmodified Risk Factors. Re-trieved May 20, 2017, from http://www.who.int/.


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http://www.euro.who.int/__data/assets/pdf_file/0008/130040/E74339.pdf

http://www.euro.who.int/__data/assets/pdf_file/0008/130040/E74339.pdf

http://www.who.int/


Epidemic Model of Co�infection ofDengue and Chikungunya

Edwin Setiawan Nugraha1, Karunia Putra Wijaya2, Thomas Gotz2, Nuning Nuraini1,Edy Soewono*1⇤

1Department of Mathematics, Institut Teknologi Bandung, 40132 Bandung, Indonesia2Mathematical Institute, University Koblenz�Landau, 56070 Koblenz, Germany


Abstracthealth problems such as co�infection. Clinical conditions for co�infection are generallymore severe than dengue or chikungunya infections. Information about long termbehaviour of co�infection transmission is still limited and not much reported. Here, wepropose an SIR�SI model of dengue and chikungunya epidemic in which co�infectionoccurs only in humans. In this model, co�infection occurs only through reinfection withchikungunya during the infection with dengue or though reinfection with dengue duringthe infection with chikungunya. The basic reproduction number is obtained analyticallyby using the next generation matrix. Stability of disease�free and single endemicequilibria are shown analytically. Further, complex behaviour of the co�existence equi-librium is shown numerically. The existence Hopf bifurcation, calculation of Lyapunovexponent and the corresponding limit cycle are also done numerically.

Keywords: (Dengue, Chikungunya, Co�infection, Mathematical modelling, Basicreproduction number.)

References1. Esteva, L., & Vargas, C. (1999). A model for dengue disease with variable human

population. Journal of Mathematical Biology, 38(3), 220�240.

2. Esteva, L., & Vargas, C. (2003). Coexistence of different serotypes of dengue virus.Journal of Mathematical Biology, 46(1), 31�47.

3. Aguiar, M., Kooi, B. W., Rocha, F., Ghaffari, P., Stollenwerk, N. How much com-plexity is needed to describe the fluctuations observed in dengue hemorrhagic feverincidence data?. Ecological Complexity 16, 31�40.


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Imitation Game Dynamics onVaccine�Decision Making Behaviouron Dengue Transmission Dynamics

Meksianis Ndii1⇤, Nursanti Anggriani2, Asep Supriatna21 Universitas Nusa Cendana, Indonesia2Universitas Padjadjaran, Indonesia


AbstractAlthough dengue vaccine is available and it is efficacious among children who areseropositive, there remain questions about its effects on long-term. Given that theinformation around its long-term effects is not widely known, this may affect anindividuals decision on the use of dengue vaccine. In this talk, we present the impact ofindividual vaccine decision�making behaviour on disease transmission dynamics. Basedon game theory, we develop a mahematical model and theoretically assess the impactof an individuals decision on the use of dengue vaccine on dengue transmission dynamics.

Keywords: (Dengue, Vaccine, Imitation dynamics )


51


Exploration on Virus Transmissionusing Complex Networks: Pandemic

Flu in Los AngelesAndreas M.M. , Ari Juanda, Febi Andhika, Haris Bhakti Permana, Prama Setia Putra⇤,

Nuning NurainiDepartment of Mathematics, Institut Teknologi Bandung, 40132 Indonesia


AbstractVirus is a parasite which can spread through human interactions. This thing can be verydangerous to human life because it causes many diseases. There was a science-fictionfilm which depicted the propagation of deadly virus known as Pandemic Flu or SpanishFlu in Los Angeles. This film exhibited the spread of virus between some regions in LosAngeles and the source of infection was identified in the end of the film. On differentway to the film plot, the objectives of this modelling are to perform the simulation ofvirus spread on 30 locations in Los Angeles and to analyze the effect of network selectiontowards virus spreading on those 30 locations. There are two networks approaches toperform the modelling of virus spreading which are distance-based network and scale-free network. Scale-free network structure shows faster time to spread the virus amongdifferent locations than distance-based network. Time of virus spread is determinedthrough two patches SIS model.

Keywords: (Virus, Pandemic flu, SIS model, Distance�Based network, Scale�Freenetwork)


52


Optimal Fish Harvesting Strategy usingForward�Backward Sweep Method

Nailul Izzati⇤, Imamatul UmmahFaculty of Engineering, Hasyim Asyari University


AbstractOverfishing are one of worldwide environmental issues. Indonesia, as maritime country,is facing the same problem. In 2015, according to Division Head of Capture Fisheriesof Marine and Fisheries Office of East Java, Eryono, the exploitation that occures inJava Sea reached 95% of its total potential [1]. To overcome this situation, Ministryof Maritime Affairs and Fisheries Republic of Indonesia decide to announce MinistrialRegulations MMAF No. 2 Year 2015 that forbid non-eco-friendly catching tools, andrecommend the friendly one [2]. But up until 2018, this regulation is rejected by mostof the fishermen that operate in Java Sea, because it need a huge fund to switch theircatching tool to another one, and the revenue they yielded by using the recommended oneis not profitable. So that, it is required to have another strategy to deal with this problem.In this study, we propose a harvesting strategy to achieve sustainable fishing in Indonesia.The aim of this study is to obtain an optimal harvesting strategy by considering fishharvesting restriction and taxation as control variables, with objective to maintain the op-timality of fish population and the fishermen income. We purpose Pontryagin MaximumPrinciple [3] to get the characteristic of optimal control problem solution analitically. Thecharacteristic obtained are numerically simulated by Forward�Backward Sweep Method[4]. Using Pontryagin Maximum Principle in the optimal control problem, we obtainthe optimal fish harvesting strategy which is characterized by bang-bang and singularcontrol, and its switching function. Numerical simulation showed that the optimal fishharvesting strategy obtained could optimize the fish population and net revenue of thefishermen.

Keywords: (Bang�bang control, Fish harvesting mathematical model,Forward�Backward sweep method, Pontryagin maximum principle, Switching function.)

References1. Hazliansyah, H. & Lukmansyah, O. (2015, March 24)Pemanfaatan Potensi

Ikan Laut Jawa Melampaui Batas. Retrieved April 11, 2017, from http://www.republika.co.id/berita/nasional/daerah/15/03/24/nlpkty-pemanfaatan-potensi-ikan-laut-jawa-melebihi-batas.

2. Sutisna, D. (2018) Profil Pelabuhan Perikanan Nusantara Brondong Tahun 2017(Brondong National Fishing Port Profile 2017). Brondong National Fishing Port.

3. Naidu, D. S. (2003). Optimal control systems. Boca Raton, FL: CRC Press.


53

4. Lenhart, S., & Workman, J. T. (2007). Optimal control applied to biological mod-els. Boca Raton: Chapman and Hall/CRC.


54


Mathematical Model of PI3K/AKTPathway in The Absence of ProteinPhosphatase in AML Y. A. Adi1,2⇤, L. Aryati2, F.

Adi�Kusumo2, and M. S. Hardianti31Departement of Mathematics, Universitas Ahmad Dahlan, Indonesia2 Departement of Mathematics, Universitas Gadjah Mada, Indonesia

3 Department of Internal Medicine, Universitas Gadjah Mada, Indonesia


AbstractA model for PI3K/AKT pathway in Acute Myeloid Leukemia (AML) is described. Weanalyze a mathematical model for the study of the interaction between PIP3, AKT, andFOXO3a in the PI3K/AKT pathway. We assume that the biochemical reaction in thispathway following the Hills equation. To conduct the mathematical analysis, we considerthe case that the mechanism of dephosphorylation protein does not work properly.Then, we analyze the model using the stability theory of differential equations. Firstly,the existence of steady states and their stability are discussed. Secondly, numericalsimulations are given to the influence of the key parameters on the spread of AMLdisease, to support the analytical results of the model. Our results show how targettherapy can be performed on the PI3K/AKT pathway for the treatment of AML.

Keywords: (PI3K/AKT pathway, Mathematical model, Stability)

References1. Clapp, G.D. & Levy, D. (2015). A Review of Mathematical Models for Lymphoma

and Leukemia. Drug Discovery Today: Disease Models, 16,16.

2. Dohner, H.,Estey, E.,Grimwade, D. et al. (2017) Diagnosis and management ofAML in adults: 2017 ELN Recommendations From an International Expert Panel.Blood, 129(4),424�447.

3. Kadia, T.M., Ravandi, F., Cortes, J., & Kantarjian, H. (2016). New Drugs in AcuteMyeloid Leukemia. Annals of Oncology, 27, 770 778.


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Performance Comparison of theConvolutional Neural Network

Optimizer for Photosynthetic PigmentsPrediction on Plant Digital Image

K.R. Prilianti1,3,⇤, T.H.P. Brotosudarmo2, S. Anam3, A. Suryanto3

1 Department of Informatics Engineering, Ma Chung University, Indonesia2Ma Chung Research Center for Photosynthetic Pigments, Indonesia

3Department of Mathematics, Brawijaya University, Indonesia


AbstractDetermination of photosynthetic pigments in intact leaves is an essential step in the plantanalysis. Along with the rapid development of digital imaging technology and artificialintelligence, determination of plant pigments can now be done in a non-destructive andreal-time manner. In previous research, a prototype of the non-destructive and real-timesystem has been developed by utilizing the Convolutional Neural Network (CNN)model to produce predictions of three main photosynthetic pigments, i.e., chlorophyll,carotenoid, and anthocyanin. The CNN model was chosen due to its ability to handleraw digital image data without prior feature extraction. In the near future, this abilitywill be useful for developing analytical portable devices. Input of the system is plantdigital image (in RGB format), and the output are predicted pigment concentration.Convolutional Neural Network performance depends on several factors, among them aredata quality, algorithm tuning (weight initialization, learning rate, activation function,network topology, batches and epochs, optimization and loss) and models combination.The focus of this research is to improve the accuracy of CNN model by optimizing theselection for updating CNN architecture parameters which are optimization method andthe loss function. As it is already known, there is no single optimizer can outperform forall cases. The selection for the optimizer should be made by considering the variabilityof the data and the nonlinearity level of the relationship patterns that exist in the data.Because the theoretical calculation is not enough to determine the best optimizer, anexperiment is needed to see at firsthand the performance of optimizers that allegedlymatches the characteristics of the data being analyzed. Gradient descent optimizationmethod is well known for its ease of computing and speed of convergence on largedatasets. Here, 7 gradient descent�based optimizers were compared, i.e., StochasticGradient Descent (SGD), Root Mean Square Propagation (RMSProp), Adaptive Gradient(Adagrad), Adaptive Delta (Adadelta), Adaptive Max Pooling (Adamax), AdaptiveMomentum (Adam), and Nesterov Adaptive Momentum (Nadam). We proved thatAdamax and Adam was the best optimizer to improve CNN ability in handling a digitalimage-pigments content relationship.


56

Keywords: (Convolutional neural network, Digital image, Gradient descent optimizer,Photosynthetic pigments)

References1. Dyrmann, M.,Karstoft, H., & Midtiby, H. S. (2016, November). Plant Species

Classification using Deep Convolutional Neural Network. Biosystems Engineering,151, 72�80.

2. Ghazi, M. M., Yanikoglu, B., & Aptoula, E. (2017,April) Plant Identification usingDeep Neural Networks via Optimization of Transfer Learning Parameters. Neuro-computing, 235, 228235.

3. Engilberge, M.,Collins, E. & Susstrunk, S. (2017) Color Representation in DeepNeural Networks. IEEE International Conference on Image Processing.

4. Ruder, S. (2016). An Overview of Gradient Descent Optimization Algorithms.arXiv preprint. arXiv:1609.04747.

5. Thoma, M. (2017). Analysis and Optimization of Convolutional Neural NetworkArchitectures. Master Thesis: Institute for anthropomatics and FZI Research Centerfor Information Technology.

6. Prilianti, K. R., Onggara, I. C., Adhiwibawa, M. A. S., Brotosudarmo, T. H. P.,Anam, S. & Suryanto, A. (2018). Multispectral Imaging and Convolutional NeuralNetwork for Photosynthetic Pigments Prediction. in IEEE International Conferenceon Electrical Engineering. Computer Science, and Informatics(in press).


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Mathematical Model of DengueTransmission with Mobility Aspect

Muhammad Fakhruddin⇤, Nuning Nuraini, Edy SoewonoDepartment of Mathematics, Institut Teknologi Bandung, 40132 Bandung, Indonesia

⇤m [email protected]

AbstractDengue is one of the most viral vector-borne diseases in the world. One of the drivingfactors of dengue transmission is human mobility either on a local or global scale.Mobility of people at a large scale could transmit dengue viruses from an endemic areato a non-endemic area and possibly increase the endemicity in both areas. In this study,we investigate the role of human mobility in the dynamics of dengue transmission withan SIR�SI type model. Two options in reducing the model are presented to reduceunobserved parameters. We do parameter estimation based on dengue incident data.Furthermore basic reproduction ratio, stability of coexistence equilibrium, and sensitivityanalysis are presented with respect to mobility rates.

Keywords: (Dengue transmission, Mobility, Parameter estimation)

References1. Driessche, P. V., & Watmough, J. (2002). Reproduction numbers and

sub�threshold endemic equilibria for compartmental models of disease transmis-sion. Mathematical Biosciences, 180(1-2), 29�48.

2. Esteva, L. & Vargas, C. (1998). Analysis of a dengue disease transmission model.Mathematical biosciences, 150, 131�151.

3. Pandey, A., Mubayi, A., & Medlock, J. 2013. Comparing vectorhost and SIR mod-els for dengue transmission. Mathematical biosciences, 246, 252�259.


58


The Helicoverpa Armigera SpreadControlling Model on The Glycine Max

Growth using Zea Mays LS. I. Lestari ,J. W. Puspita⇤, R. Ratianingsih⇤

Mathematics Study Program Tadulako University

⇤[email protected], [email protected]

AbstractThis paper discusses the pest spread problem founded in the growth of Glycine Max thatdisturbed by Helicoverpa attack. To divert the pest, Zea Mays L is proposed to protectthe Glycine Max growth. An interaction scheme is constructed by consider the life cycleof Helicoverpa Armigera, Glycine Max and Zea Mays. The scheme is used as the basisof a mathematical model that describe the interaction among the related subpopulation.The stability of the the model is analysed by linearization method at the endemic criticalpoint. An asymptotic stable critical point shows that the zea mays successes to overcomethe pest attack.

Keywords: (Glycine max, Helicoverpa armigera, Linearization method, Mathematicalmodel, Zea Mays L)

References1. Champbel, S. L. , & Haberman, R. (2008). Introduction to Differential Equations

with Dynamical System. NewJersey: Princeton University Press.

2. Cordeiro Albernaz,K., Vivan, L. M. , Gui�maraes, H. O. , & Carvalhais, T. (2013).First occurrence record of Helicoverpa armigera (Hubner)(Lepidoptera: Noctuidae)no Brasil. Pesq. Agropec. Trop., Goiania, 43(1),110-113.

3. Khan, Z. R., C. A. O Midega, N. J. Hutter, R. M. Wilkins, & Wadhams, L. J. (2006).Assessment of the potential of Napier grass (Pennisetum purpureum) varieties as atrap plants for management of Chilo partelus. Entomologia Ex�perimentalis etApplicata


59


SIR�SI Model for Malaria Disease withTreatment and Vector Control

Kemal Adam Roisy⇤, Dr. Dipo AldilaDepartment of Mathematics, Universitas Indonesia


AbstractIn this talk, a mathematical model of malaria with intervention of fumigation (u1) andmedical treatment (u1) will be discussed. Equilibrium points and their stability areanalyzed analytically and numerically. Basic reproduction number (R0) of the model hasbeen determined with Next Generation Matrix approximation. We found that if R0 > 1,then we have an endemic equilibrium. While if R0 > R

⇤, we only have a diseasefree equilibrium, where R

⇤ is the threshold of the back�ward bifurcation. A backwardbifurcation appears when R

⇤< R0 < 1, which arise two endemic equilibrium points.

Some numerical simulations for the bifurcation and the autonomous model is given inthe end of the talk.

Keywords: (Malaria, Backward bifurcation, Fumigation, Medical treatment, SIR�SImodel)

References1. Castillo�Chavez, Carlos, Baojun Song. (2004). Dynamical Models of Tu-

berculosis and Their Applications. Mathematical Bioscience and Engineering,2(1),361�404.

2. Diekmann, O., Heesterbeek, J. A. P. & Roberts, M. G. (2010). The Constructionof Next� Generation Matrices for Compartmental Epidemic Models. J. R. Soc.Interface, 7,873�885.

3. Lynch, S. (2000). Dynamical Systems with Applications using Maple (2nd Ed.).Boston: Birkhauser, Springer Science.

4. Strogatz, S.H. (1994). Nonlinear Dynamic and Chaos with Applications to Physics,Biology, Chem- istry and Engineering. Massachusetts: Perseus Books Publishing,L.L.C.

5. Xiaomei Feng, et al. (2015). Stability and Backward Bifurcation in A MalariaTransmission Model with Applications to The Control of Malaria in China. Math-ematical Bioscience, 266, 52�64.


60


Modeling of Rabies TransmissionDynamic between Human and Dogs

with the Effect of ImmunocontraceptiveVaccine

Eti D. Wiraningsih1,⇤, Asep K. Supriatna21Department of Mathematics, Faculty of Mathematics and Natural Sciences, State

University of Jakarta, DKI-Jakarta, Indonesia address2 Department of Mathematics, Faculty of Mathematics and Natural Sciences, University

of Padjadjaran, Bandung-West Java, Indonesia


AbstractWe formulated a deterministic model for the transmission dynamics of rabies virus inthe dogs-human zoonotic cycle. The effect of immunocontraceptive vaccine in dogsis considered on the model, then the stability was analysed to get basic reproductionnumber. We use the next generation matrix method to analyze the stability of the DiseaseFree Equilibrium of this model.

Keywords: (Stability analysis, Rabies model, Immunocontaceptive vaccine.)

References1. Yang, D., Kim, H., Lee, K., & Song, J. (2013). The present and future of rabies

vaccine in animals. Clinical and Experimental Vaccine Research, 2, 19-25.

2. Dwipedi, J. & Sachdev, Y., (2012). Advents in contraception: immunocontracep-tion. International Journal of Therapeutic Applications 1, 5-19.

3. Hanlon, C. A. & Rupprecht, C.E., (1993). Considerations for immunocontraceptionamong free�ranging carnivores: The rabies paradigm. Contraception in WildlifeManagement, Paper 11.

4. Lakshmikantham, V., Leela, S., & Martynyuk, A.A., (1989). Stability analysis ofnonlinear systems. New York: Marcel Dekker, Inc.

5. Muller, L.I., Warren, R.J. & Evan, D.L, (1997). Theory and Practice of Immuno-contraception in Wild Mammals. Wildlife Society Bulletin, 25(2), 504�514.

6. Smith, G.C. & Cheeseman, C. L. (2002). A mathematical model for the control ofdiseases in wildlife populations: culling, vaccination and vertility control. Ecolo-gycal modelling, 150,45�53.


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7. Driessche, P. V., & Watmough, J. (2002). Reproduction numbers andsub�threshold endemic equilibria for compartmental models of disease transmis-sion. Mathematical Biosciences, 180(1-2), 29�48.

8. Wu, X., Franka, R., Svoboda, P., Pohl, J. & Rupprecht, C.E. (2009). Develop-ment of combined vaccines for rabies and immunocontraception. Vaccine, 27,7202�7209.

9. Wu, X. & Rupprecht, C.E. (2011). Rabies virus based-recombinant immunocontra-ceptive compositions and methods of use. United States patent Aplication Publica-tion.


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Mathematical Model of Zika VirusTransmission with Saturated Incidence

RatePuji Andayani1,⇤, Lisa Risfana Sari1, Agus Suryanto2, Isnani Darti2

1Universitas Internasional Semen Indonesia2 Department of Mathematics, Brawijaya University


AbstractZika virus is a type of virus lead by Aides Aegyepti mosquitoes. This virus is potentiallyspread in the tropics area. Long-term effects of the Zika virus are quite harmful,including of hydrocephaly and GBs. Mathematical models have a very important rolein the case of disease spread. In this paper, we propose and analyze the model of Ziavirus transmission with saturated incidence rate. This model consists of five nonlinearordinary differential equations which are reducing to be three nonlinear equations. Themathematical model obtained will be analyzed dynamically. Analytically in disease freecondition, it is persuaded mortality which is shown that the disease free equilibrium islocally asymptotically stable when the reproduction number is less than unity. Otherwise,the endemic equilibrium stable. Further, the numerical simulation used to explore thebehavior of equilibrium of the system.

Keywords: (Zika transmission, Saturated incidence rate, Reproduction number)

References1. Agusto, F., Bewick, S., & Fagan, W. (2017). Mathematical Model for Zika virus

dynamics with sexual transmission route. Ecological Complexity, 29, 61�81.

2. Kaddar, A. (2009). On The Dynamics of A Delayed SIR Epidemic Model With AModified Saturated Incidence Rate. Electronic Journal of Differential Equations,2009, 1�7.

3. Global dynamics of vector�borne disease with horizontal transmission in host pop-ulation. Computers and Mathematics with Applications, 745�754.

4. Xiao, D., & Ruan, S. (2007). Global analysis of an epidemic model withnon�monotone incidence rate. Math. Bioscience, 419�429.


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Modeling The Spread of BacterialResistance in Hospital

Nela Rizka, Mochamad Apri, Pratiwi WikaningtyasBandung Institute of Technology, Indonesia


AbstractAntibiotic resistance is the ability of bacteria to avoid or inhibit attacks from antibiotics.The phenomenon of the spread antibiotic resistance has increased significantly, especiallyin hospitals. The negative impacts arising from these phenomena include the hightreatment cost and high mortality rates of patients due to infectious disease. In responseto these problems, this work proposed a model of spread bacterial resistance in hospitals.From analysis of model, we obtained that the spread of bacterial resistance in the hospital,at the end, still occur even though the patient get antibiotics therapy. Meanwhile, if thepatient’s level of awareness to keep themselves from resistant bacterial contamination isconsidered, then the spread of resistance in the hospital can be controlled. The higher thelevel of patient awareness the smaller the spread of resistance occurs.

Keywords: (Ordinary differential equations systems, The spread of bacterial resistance,Antibiotics )


64


Blighted Ovum Detection Using DeepConvolution Neural Network Method

Feni Andriani⇤, Iffatul MardhiyahGunadarma University


AbstractBlighted Ovum is a state of conception that contains no fetus. Early detection of BlightedOvum may reduce the risk of miscarriage. One tool that can be used in the detection ofBlighted Ovum is by using ultrasonography. However, the detection of Blighted Ovumthrough ultrasound image is still difficult, because it is still very dependent on the levelof knowledge and subjectivity of medical experts. One of the most successful ultrasoundimage detection or classification methods is Deep Learning. Deep learning is growingrapidly due to the development of Graphical Processing Unit (GPU). One of the bestmachine learning methods in terms of image classification by utilizing GPU is calledDeep Convolutional Neural Network method. This method consists of three stages. Thefirst stage is the feature extraction of ultrasound image data. The second stage of thelearning phase or training by using feedforward and backpropagation methods. The thirdstage is the phase of image classification using feedforward method. This research willdevelop an automatic classification algorithm on the ultrasound examination result usingDeep Convolutional Neural Network in Blighted Ovum detection. This study is alsoexpected to assist medical experts in providing quick and accurate decisions on whetheror not Blighted Ovum is present, so fetal rescue is not too late. the accuracy of thealgorithm implementation is 80%.

Keywords: (Blighted ovum, Deep learning, Graphical processing unit miscarriage,Ultrasound)

References1. Coates, A., Lee, H. & Ng, A. Y., (2011). An Analysis of Single-Layer Networks in

Unsupervised Feature Learning.

2. Stathakis, D. (2008). How Many Hidden Layers And Nodes?. International Jour-nal of Remote Sensing.

3. Krizhevsky, A. (2013). ImageNet Classification with Deep Convolutional NeuralNetworks.


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Mathematical Model for Rise and FallArmy Population

Anita Triska⇤, Heni Widayani, Nuning NurainiIndustrial and Financial Mathematics Research Group, Faculty of Mathematics and

Natural Sciences, Institut Teknologi Bandung,


AbstractAn armed force is a professional organization formally authorized by a sovereign stateto use deadly force and weapons to support sovereignty of the state. It typically consistsof Army, Navy, Air Force, and Marines. One of their main tasks is assigned in wareither to defend their state independence or just for political reason. Recruitment rateof military member is an important to ensure the sustainability of this military system.This study construct mathematical model which give the dynamics of citizen and armypopulation. The first model involves systems of time�dependent ordinary differentialequation. Dynamical analysis such as existence and stability of equilibrium point areobtained. Threshold value for stability of each equilibrium point can be biologicallyinterpreted. The model was developed into a partial differential equation which is timeand space�dependent. The second model is represented with reaction�diffusion modelwith self and cross diffusion. Two different boundary conditions are implemented for thearmy population which will be illustrated in numerical simulation.

Keywords: (Army, War, Dynamical population model)

References1. Barnes, B. & Fulford, G. R. (2015). Mathematical Modelling with Case Studies:

Using Maple and MATLAB,(3rd ed.). Taylor and Fracis Group Ltd.

2. Correlli Barnett. (1970). Britain and her army, 1509-1970: a military, political andsocial survey, 90�98, 110�125.

3. Goodwin and Jason (1998). Lords of the Horizons: A History of the Ottoman Em-pire. New York: H. Holt, 59,179�181.

4. Lord, Kinross. (1977). Ottoman Centuries: The Rise and Fall of the Turkish Em-pire. New York: Morrow Quill Paperbacks, 52.


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Stability of Hepatitis B Virus Modelwith Cure and Absorption Effect

Lisa Risfana Sari⇤, Puji AndayaniUniversitas Internasional Semen Indonesia

⇤Universitas Internasional Semen Indonesia

AbstractConsidering hepatitis B as one of challenge to public health, we introduce a modifiedmathematical model of hepatitis B infection with cure and absorption effect. There aretwo equilibria, virus free equilibrium and endemic equilibrium. Numerical simulationsindicate that the basic reproductive ratio is related to the existence condition of endemicequilibrium. If the basic reproductive ratio is less than one then virus free equilibriumis established, while if the basic reproductive ratio is greater than one then endemicequilibrium is established. Numerical simulations suggest that immune response have arole to control the infection.

Keywords: (Absorption effect, Cure, Hepatitis B virus, Reproduction number.)

References1. Dubey, B., Dubey, P., & Dubey, U. S. (2016). Modeling the intracellular pathogen-

immune interaction with cure rate. Communications in Nonlinear Science and Nu-merical Simulation, 38, 7290. https://doi.org/10.1016/j.cnsns.2016.02.007

2. Manna, K., & Chakrabarty, S. P. (2015). Chronic hepatitis B infec-tion and HBV DNA-containing capsids: Modeling and analysis. Com-munications in Nonlinear Science and Numerical Simulation, 22, 383395.https://doi.org/10.1016/j.cnsns.2014.08.036

3. Wang, K., Fan, A., & Torres, A. (2010). Global properties of an improved hep-atitis B virus model. Nonlinear Analysis: Real World Applications, 11, 31313138.https://doi.org/10.1016/j.nonrwa.2009.11.008


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Optimal Control of Innate ImmuneResponse in Infected

Lung�Macrophages by StreptococcusPneumoniae

Usman Pagalay⇤, Dewi Zumrotul Nafisa, Heni WidayaniDepartment of Mathematics, Mathematics State Islamic University Maulana Malik

Ibrahim Malang


AbstractInnate immune response in lung macrophages can be modeled as a system of first ordernonlinear differential equations. This model consists of bacterial Streptococcus Pneumo-niae populations, inactive macrophages, and active macrophages. We performed optimalcontrol using Pontryagin Minimum Principle and simulated using finite difference andRunge Kutta fourth order. The results show either bacterial growth using control or not.This growth is suppressed by proinflammatory cytokines. If an individual has a goodimmune system then growth time of bacteria streptococcus pneumoniae becomes slower.Further, if an individual has a bad immune system, then growth time becomes faster.

Keywords: (Innate immune, Lung macrophages, Streptococcus Pneumoniae, Optimalcontrol)

References1. Hottlinger, E.D. (2017). Mathematical Modelling of Strepcoccus Pneumoniae Col-

onization, Invasive Infection and Treatment. Article 115 frontiers in Physiology, 8.London.

2. Itik, M. (2016). Optimal Control of Nonlinear Systems with Input Constraints us-ing Linear Time Varying Approximations. Nonlinear Analysis : Modelling andControl, 21(3),400�441.

3. Smith, et al. (2011). Mathematical Model of a Three-Stage Innate ImmuneResponse to a Pneumococcal Lung Infection. Jurnal of Theoretical Biology,276(2011),106�116.

4. Tu, P.N.V. (1984). Introduction Optimazation Dynamic: Optimal Control with Eco-nomics and Management Applications. Berlin: Springer-Verlag.


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Parameter Estimation of ExternalForced Oscillation of Fuzzy Duffing

Equation: Numerical Performance byExtended Runge�Kutta Method

Muhammad Ahsar Karim 1,2,⇤, Agus Yodi Gunawan1, Mochamad Apri1, and KuntjoroAdji Sidarto1

1Department of Mathematics, Faculty of Mathematics and Natural Sciences, InstitutTeknologi Bandung, Jl. Ganesha 10 Bandung, Indonesia

2Permanent Address: Program of Mathematics, Faculty of Mathematics and NaturalSciences, Universitas Lambung Mangkurat, Jl. A. Yani Km. 36 Banjarbaru, Indonesia

⇤m [email protected]

AbstractIn general, most of systems biology may contain uncertainties, either on structuresor parameters. These uncertainties are possibly either due to limitations of availabledata, complexity of the systems, or environmental or demographic changes. One oftypical behavior that commonly appears in the systems biology is a periodic behavior.Mathematical model of the system with periodic behavior often exhibit complex dynamicbehaviors, depending on the initial values and parameters. By accommodating uncer-tainties in the model, it certainly requires an intensive study in terms of mathematicalstructures descriptions, methodologies for determining solutions and procedures forparameter estimations. One of the mathematical models that describes periodic behavioris External Forced Oscillation of Fuzzy Duffing Equation. In this work, the modelwill be considered as our subjects by assuming that the initial values have uncertaintiesin terms of Fuzzy Numbers. The resulted fuzzy models will be studied by two fuzzydifferential approaches, namely Hukuhara Differential and Fuzzy Differential Inclusions.Applications of Fuzzy Arithmetic to the model leads us into Alpha-Cut DeterministicSystems, with some additional equations. These systems are then solved by ExtendedRunge-Kutta Method. In contrast to the standard Runge-Kutta Method, the extendedRunge-Kutta method utilizes new parameters in order to enhance the order of accuracy ofthe solutions by including both function and its first derivative values in the calculations.Among those fuzzy approaches, Fuzzy Differential Inclusions is the most appropriateapproach to capture periodic behaviors of the model, using extended Runge-Kuttamethod. Finally, we demonstrate how to estimate parameters using Fuzzy DifferentialInclusions to our generated fuzzy simulation data.

Keywords: (External forced oscillation of fuzzy duffing equation, Hukuhara differential,Fuzzy differential inclusions, Extended Runge�Kutta method, Parameter estimation)

References


69

1. Karim, M. A., Gunawan, A. Y., Apri, M., &c Sidarto, K. A. (2017). Solving a fuzzyinitial value problem of a harmonic oscillator model. AIP Conference Proceedings1825, 020011. doi:10.1063/1.4978980

2. L.A. Zadeh. (1965). Information and Control, Fuzzy Sets, 8, 338�353.

3. S.L. Chang & L.A. Zadeh. (1972) IEEE Trans, Systems Man Cybernet, On FuzzyMapping and Control, 2, 30�34, . doi: 10.1109/TSMC.1972.5408553.

4. Ghanaie, Z.A. & Moghadam, M. M. (2011). The Journal of Mathematics and Com-puter Sciences, Solving Fuzzy Differential Equations by Runge�Kutta Method, 2(2), 208�221.

5. T. Jayakumar, D. Maheskumar, and K. Kanagarajan. (2012). Applied Mathemati-cal Sciences. Numerical Solution of Fuzzy Differential Equations by Runge�KuttaMethod of Order Five, 6 (60), 2989-3002.


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Global Stability of The Disease FreeEquilibrium in A Cervical Cancer

Model: A Chance to RecoverLina Aryati 1 , Tri Sri Noor Asih2, Fajar Adi�Kusumo1,⇤, Mardiah Suci Hardianti4

1Department of Mathematics Faculty of Mathematics and Natural Sciences UniversitasGadjah Mada Indonesia

2Department of Mathematics Faculty of Mathematics and Natural Sciences SemarangState University Indonesia

4Faculty of Medicine Universitas Gadjah Mada Indonesia

⇤f [email protected]

AbstractWe consider a cervical cancer model with a treatment focusing on the precancerous cells.As one of the objectives of treatment is dealings with recovery, in this paper, we givethe sufficient conditions for the disease free equilibrium to be globally asymptoticallystable. These conditions hopefully could guide us in the effort of healing. We also givenumerical simulation to illustrate the dynamic of recovery process.

Keywords: (Cervical cancer, Disease free equilibrium, Global stability.)

References1. Noor�Asih,T. S., Lenhart, S., Wise, S., Aryati, L., Adi-Kusumo, F., Hardianti, M.

S. & Forde, J.(2016). The dynamic of HPV infection and cervical cancer cells,Bulletin Mathematics Biology, 78,4�20.

2. Noor�Asih,T. Adi�Kusumo, F., Aryati, L., & Hardianti, M. S. (2015). The metas-tasis behavior in cervical cancer model. Far East J. Math. Sci. (FJMS), 96(8),981�990.

3. Sanga, G. G., Makinde, O. D., Massawe, E. S., & Namkinga, L.(2017). Modelingco�dynamics of cervical and HIV disease. Global J. Pure Appl. Math., 13(6),2057�2078.


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Minimizing Parameter and DynamicalUncertainties in Biological Models

Levina Michella ⇤, Mochammad ApriInstitut Teknologi Bandung


AbstractMathematical model of a biological phenomenon contains parameters related to theinteractions in the biological systems. Some of these parameters may have to be estimatedfrom experimental data. However, due to some constraints, data that can be obtainedfrom experiments are limited. Thus, if the data is not informative, this limitation leadsto large parameter and dynamical uncertainties in biological models. Consequently, thebehavior of the model will be elusive. Here we propose several strategies to performinformative experiments to reduce the uncertainties. Given a few experimental data,in our work, parameter estimation is carried out numerically by Controlled RandomSearch method. This yields an ensemble of parameter estimates. Based on this estimates,the times that give the highest dynamical uncertainty are chosen to indicate the time atwhich measurements have to be done. In addition, we also look for some experimentalconditions that can falsify the obtained estimates. This is conducted by finding theconditions that give the highest dynamical uncertainty. In this way, the parameter anddynamical uncertainties of the model can be reduced efficiently.

Keywords: (Biological model, Parameter estimation, Controlled random search, Param-eter uncertainty, dynamical uncertainty)

References1. El�Samad, H., Prajna, S., Papachristodoulou, A., Doyle, J., & Khammash, M.

(2006), Advanced Methods and Algorithms for Biological Network Analysis, Pro-ceedings of the IEEE, 94, 832�853.

2. Mdluli, T., Buzzard, G.T., & Rundell, A.E. (2015). Efficient Optimization of Stimulifor Model- Based Design of Experiments to Resolve Dynamical Uncertainty. PublicLibrary of Science Computational Biology.

3. Price, W.L. (1983). Global Optimization by Controlled Random Search. Journal ofOptimization Theory and Applications, 40, 333�348.

4. Raue, A., Kreutz, C., Maiwald, T. Bachmann, J., Schilling, M., Klingmuller, U.& Timmer, J. (2009). Structural and practical identifiability analysis of partiallyobserved dynamical models by exploiting the profile likelihood. Oxford UniversityPress,1923�1929.


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A Fuzzy Basic Reproduction Numberfor A Fuzzy Smoker Growth Model

Herlinda Nurafwa Sofhya⇤, Agus Yodi GunawanInstitut Teknologi Bandung, Indonesia


AbstractConsumption of a large amount of cigarretes in a public society is one of the mainconcerns in every countries since cigarettes may become the source of all dangerousdiseases, like TBC, Cancer and many other health and social problems. Many programshave been simulated by government to overcome smoking problems. One of importantthings for the goverment is to predict smokers growth population. In this paper, we derivea smoker growth model in which the population is classified by three sub populations: apotential smoker, an active smoker, and a quitted smoker. Commonly, the transmissionrate in the classical model is assumed to be constant. However, in reality the transmissionamong them may depend on age of smoker. To get insight into this, the transmissionrate will here be relaxed to be dependence of ages and contain uncertainty that isconsidered as a triangular fuzzy number. Our main focus will be paid into determinationof fuzzy basic reproduction number through fuzzy expected value concept. Using theresulted fuzzy basic reproduction number, we calculate the critical age smoker abovewhich the endemic case takes place. It turns out this critical age is less than that ofresulted from the classical (non-fuzzy) basic reproduction number. It means that fuzzysmoker growth model may be considered as an early warning model for the endemic case.

Keywords: (Smoker growth model, Fuzzy number fuzzy, Expected value, Basic reproduc-tion number, Endemic )


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Protein Sequence Analysis of The ZikaVirus and The Dengue Virus Using

Smith Waterman AlgorithmMohammad Syaiful Pradana⇤, Siti Amiroch

Department of Mathematics, Faculty of Mathematics and Natural Sciences UniversitasIslam Darul ’Ulum Lamongan, Indonesia

⇤[email protected]. id

AbstractZika virus that had a warm conversation in the media last year is very interesting to study,especially because the Zika virus caused symptoms similar to dengue fever. The virusis transmitted to humans by mosquitoes of the genus Aedes, principally Aedes aegyptimosquitoes in tropical regions is the same that transmits dengue, chikungunya and yellowfever.In Brazil, local health authorities have observed an increase syndrome Zika virusinfection in the community, as well as an increase in babies born with microcephaly(enlarged head) in northeast Brazil. In addition, more than 13 countries in the Americashave reported sporadic Zika virus infection that show very rapid geographic expansion.While in Indonesia, the euphoria is also increasingly prevalent virus discussed especiallyafter the discovery of Jambi positive patients infected with the virus Zika on January 26,2016 last.Moving on from this, the authors wanted to know how the sequences protein zikavirus when compared with the dengue virus, the percentage of identical as well as thecalculation of local alignment its using the Smith Waterman algorithm. In addition it willalso be known genetic mutations that occur in zika virus from its origin until zika virusinto Indonesia and phylogenetic tree spread of the virus to get to Jambi.By using matlab programming, systems designed user interface that is used for sequencealignment using the Smith Waterman algorithm, as well as link to the system comes withthe browser as an option for online data retrieval. From the results obtained in matlabalignment between sequences identical values of precision turned out higher than withBLAST. Likewise, the time duration shorter Matlab simulation results compared with theoutput of BLAST

Keywords: (Sequence Analysis, Zika virus, Dengue virus, Smith Waterman algorithm)

References1. Amiroch, S. & Rohmatullah, A. (2017). Determining Geographical Spread Pattern

of MERS-CoV by distance method using Kimura Model. AIP Conference Proceed-ings, 1825(1), 020001.


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2. Irawan, I. & Amiroch, S. (2015). Construction Of Phylogenetic Tree Us-ing Neighbor Joining Algorithms To Identify The Host And The Spreading OfSARS Epidemic. Journal of Theoretical and Applied Information Technology,71(3),424�429.

3. National Center for Biotechnology Information (NCBI). Retrieved February 19,2016, fromhttp:/www.ncbi.nlm.nih.gov.

4. Perkasa, et al.(2016, February 4). Isolation of Zika virus from Febrile Patient In-donesia. Emerging Infectious Disease Journal, 22.

5. Shen, SN. (2007). Theory and mathematical methods for bioinformatics. Biologi-cal and Medical Physics, Biomedical Engineering, Springer.


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Mathematical Modeling of PanamaDisease Infection inside Banana LeavesMochamad Apri⇤, Husna Nugrahpraja, Mudita Gunawan, Gandhiano Putera, Monica

Reynata Sulaeman, Marcelino Wijaya, Joanne Immanuela RachmanDepartment of Mathematics, Institut Teknologi Bandung


AbstractPanama disease is lethal fungal disease that attacks the root and leaves of Banana plant. Itis caused by Fusarium Oxysporum f.sp. Cubense which infects and inhibits the plant fromgetting enough nutrients. As a result, the old leaves become yellow, wilt, and collapse,which eventually leads to the death of the plant. To understand the mechanisms of theinfection, in this work we develop a mathematical model that describes the interactionsbetween the fungus and proteins that play role in the leaves growth during the infection.The model consists of a set of nonlinear differential equations. The equilibrium pointsand their stability are analyzed and a numerical simulation will be presented.

Keywords: (Panama disease, Banana leaf, Mathematical model, Differential equation )


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