Epidemic and Endemic Outbreak Simulator:A Global Stochastic Cellular Automata Approach

Presented by: Hector Cuesta-ArvizuAdvisor: Armin R. Mikler

Center for Computational Epidemiology and Response AnalysisUniversity of North Texas

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Outline

Introduction (why this is important?).

Infectious Disease Model SEIR.

Infectious Disease Model SEIRS.

Cellular Automata (...the computational part).

Global Stochastic Contact Model.

Outbreak Simulator.

Vaccination Strategies.

Conclusions.

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Introduction

Why is this important?

The epidemiologist use Models to study the spread of an Infectiousdisease outbreak.

These Models include, Mathematical, Statistical and Computationalapproaches.

Simulating these models is the way that epidemiologist can observedifferent outbreak outcomes.

With the simulation we can try different interventions strategies thataffects the prevalence of an Epidemic or Endemic outbreak.

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Infectious Disease Models

Infectious Disease Models

SEIR Susceptible-Exposed-Infected-Recovered

The SEIR models the shift of individuals’ status between four states:susceptible (S), exposed (E), infected (I), and recovered (R). Each ofthose variables represents the number of people in those groups.

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Infectious Disease Models

Infectious Disease Models

SEIRS Susceptible-Exposed-Infected-Recovered-Susceptible

The SEIRS differs from the SEIR model by letting recoveredindividuals lose their resistance over time.

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Cellular Automata

Cellular Automata

What is a Cellular Automata?

Discrete model studied in computability theory and mathematics for anon-linear problems.

Facts:

It consist of an infinite, regular grid of cells, each in one of a finitenumber of states.The grid can be any finite number of dimensions.Each cell is a particular individual o group.

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Cellular Automata

Cellular Automata

Neighbourhood

The Neighbourhood is a selection of cells relative to some specifiedcell and does not change.

Each cell has the same rules for updating based on the values in thisneighbourhood.

Each time the rules are applied to the whole grid a new generation isproduced.

Local an Global Neighborhoods, Von Newmnan and Moore Neighborhood

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Model

Model

The Global Stochastic Contact Model

The goal of this model is to describe the dynamics of an infectiousdisease in a close population.

The model is a human-human Global Interaction model.

Its main purpose is the realization of contacts among individuals,facilitating analysis of the spread of diseases

The cayley graph represent the global interaction between cells(individuals).

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Model

Model

The global contact interaction

Contacts per Time Step:

C = CR∗N2

Total of Contacts in the Event:

Ctot = Σtπt=1

CR∗N2

where te = (1, 2, 3, ..., n)

C = Number of interactions per each Time Step.

CR = Contact Rate.

N = Number of individual in the population.

tπ = Number of Time Steps.

Ctot = Total Number of interactions in the event

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Outbreak Simulator

Outbreak Simulator

Technological choices for the Simulator

The main contribution of this work is to present a software systemthat incorporates a global stochastic cellular automata model.

Technological Choice:

C# .NET (as a programming language)WindowsForms and MonoDesktop (to create graphic interface and gridanimations during simulations)

Modules:

The specification module.The simulation module.The visualization module.

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Outbreak Simulator

Outbreak Simulator

Specification and simulation modules

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Outbreak Simulator

Outbreak Simulator

Visualization module

In figure A we can observe the SEIR Epidemic Curve and in figure Bwe can observe the SEIRS Endemic Curve.

(A)

(B)

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Intervention Strategies

Vaccination Strategies

Vaccination Strategies

Figure A.- Vaccination in SEIR Model

Figure B.- Vaccination in SEIRS Model

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Intervention Strategies

Vaccination Strategies

Vaccination Strategies

Scheduling Vaccination

Infected Population-Trigger Vaccination

Figure C.- Plot of Vaccination Strategies

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Conclusions

Conclusions and Future Work

Conclusions and Future Work

Simulation help to understand spread of diseases.

Also we can observe different outcomes from intervention strategies.

Future Work:

Try different kinds of contact models.Integrate Seasonality.

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Conclusions

Questions??

Questions ???

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