Evaluating strategies for pandemic response in Delhi using realistic social networks

Huadong XiaJoint work with Kalyani Nagaraj,

Jiangzhuo Chen and Madhav Marathe

NDSSL, Virginia TechICHI 2013

• Background and Contributions• Network synthesis and structure analysis• Dynamics and intervention policy• Conclusions

Outline

• Pandemics cause substantial social, economic and health impacts– 1918 flu pandemic, killed 50-100 million people or 3

to 5 percent of world population.– …– SARS 2003, H1N1 2009, Avian flu (H7N9) 2013

• Mathematical and Computational models have played an important role in understanding and controlling epidemics – controlled experiments are not allowed for ethic

consideration.– understand the space-time dynamics of epidemics

Importance of computational epidemiological models

Compartmental ModelBailey[TMTIDIA1975]

Vespignani [PNAS2006]

Evolution of computational epidemiology models

Random GraphBarrat etc.[DPCN2008]Meyers etc.[ORI2010]

Realistic networkw/ social structure

Eubank etc. [DIMACS2006]Meyers etc.[AMS2007]Barrett etc.[WSC2008]

• Recent years have seen a new approach for understanding and reasoning pertaining to epidemics– Differs from traditional approach that is based on mass action

assumptions

• Networked Epidemiology: – the main idea is that a better understanding of the characteristics of

the social contact network can give better insights into disease dynamics and effective interventions (e.g. vaccination/quarantining strategies), to control an epidemic

Networked Epidemiology

• Networks capture social interaction pertinent to the disease• We focus on flu like diseases and the appropriate network is a social contact

network based on proximity relationship.

What is a network

Edge attributes:• activity type: shop, work,

school• (start time 1, end time 1)• (start time 2, end time 2)• …

Vertex attributes:• (x,y,z)• land use• …

Locations

Vertex attributes:• age• household size• gender• income• …

People

• How do we get such a network?– In most cases we couldn’t get a precise representation of the network.

Given this we need to synthesize the network for a given region.– The type of the network one makes depends on: (i) time available to

make such a network (human and computational), (ii) the data available to make the network, (iii) the specific question that one would like to investigate

Network Synthesis

• Building on our earlier work, we propose several novel methods to develop a high resolution social contact network.– We use the new methods create a realistic social contact network for

National capital of institute.

• A detailed study to Delhi population using the generated realistic social contact network:– Detailed analysis to the static structure of the network– A high performance agent based simulation solution to study

dynamics and effects of intervention policies .– Comparison study to other cities.

Contributions

• Background and Contributions• Network synthesis and structure analysis• Dynamics and intervention policy• Conclusions

Outline

Synthetic Populations and their contact networks

Goal: Determine who are where

and when.

Process: Create a statistically

accurate baseline population

Assign each individual to a home

Estimate their activities and where these take place

Determine individual’s contacts & locations throughout a day.

Synthetic Population & Contact NetworkGeneric Methodology

Contact Network

Data

census

location

activity survey

contacts between people

contacts with durations

synthetic population

people (demographics)

locations

activities}sublocation model

gravity

People-location

GPL

• Messy data:– Multiple sources– Large scale– Unstructured and Unformatted: Region-specific, no generic solution

• Data is limited: especially for developing countries– typically only collective statistics are available– Deduce the realistic disaggregate structure out of aggregate statistics.

Challenges in network synthesis

• Case study:– Delhi (NCT-I): a representative south Asian city that was never studied

before.• Statistics:

– 13.85 million people in 2001; 22 million in 2011– Most populous metropolis: 2nd in India; 4th in the world– 573 square miles, 9 regions (refer to the pic)– The Yamuna river going through urban area.

• Unique socio-cultural characteristics: – Large slum area– Tropical weather– Environmental hygiene

Delhi: National Capital Territory of India

Data Sources and Generation Methods for Delhi Synthetic Population and Network

category Data Methods

demographicsIndia census 2001 + household

micro-data (UMD - India Human Development Survey)

distribution/IPF

geographic dataMapMyIndia: real locations, streets,

rivers Gravity model

activity

Thane travel survey decision tree + templates;

residential contact survey configuration model

Overview

• We generated synthetic population and contact network for Delhi.

• International population is hard– We develop novel method to create realistic activity templates.– Capture Spatial and demographic variation

• This social network provides useful insights toward understanding disease dynamics and intervention efficacies.

People-location network GPL: structural properties

Network No. of People No. of Locations No. of Edges

GPL 13.85M 2.72M locations(51K nonhome locations +

2.67M home locations)

28.99M

• The people-location network GPL:– The degree of a large portion of nonhome Locations have a power law

like distribution.

GPL: Temporal and spatial properties

People-people network GP

GP: local graphlets structure

Network The Delhi Network The Los Angeles Network

No. of nodes 13.85 M 16.23M

No. of edges 207 M 459 M

Average degree 29.86 56.60

Average edge weight(minute)

363 141

Average CC 0.546 0.389

Compare against another city

Disease Spread in a Social Network

• Within-host disease model: SEIR

• Between-host disease model:– probabilistic transmissions along edges of social contact

network– from infectious people to susceptible people

Public Health Interventions

• Pharmaceutical interventions: vaccination or antiviral changes an individual’s role in the transmission chain – Lower susceptibility or infectiousness

• Non-pharmaceutical interventions: social distancing measures change people activities and hence the connectivity of social network– Work closure, school closure, isolation, etc.

• Calibrate R0 to be 1.35• Vulnerability is defined as: Normalized number of infected over 10,000 runs

of random simulations

epidemic simulation results: Vulnerability

• Calibrate R0 to be 1.35

epidemic simulation results

• four different intervention strategies :– Vaccination is still most effective strategy.– Pharmaceutical interventions is more effective than the non-pharmaceutical.– School closure is more effective than work closure

epidemic simulation results: interventions

Two Versions of Delhi Networks

• Delhi v1:– Based on very limited data– Generic methodology applicable to any region in world

• Delhi v2:– Requires household level micro sample data and other detailed data,

not available for all countries

• Improvement on results is expected: V2>V1– to evaluate the network generation model;– to understand importance of different levels of details.

V1 v.s. V2: epidemic Simulations

• Impact to Epidemic Dynamics:– V1 exploited activity schedules from US survey, where people travel much more frequently than

Indian. Therefore, the two networks show very different epidemic dynamics in base case (without intervention).

– Vulnerability distribution of Delhi-V2 is flat comparing to Delhi-V1. Also, Delhi-V2 is less vulnerable than Delhi-V1, due to less frequent travel.

Epidemic Simulations: comparison of three versions

• The iterative refinement in V2 and V3 may change our decision in making intervention strategies:

– We will have very different prediction to attack rate and the peak value as well as peak date.

– In delaying outbreak of disease, school closure is more effective than Antiviral in V1, which is on the contrary in V2 and V3.

– V3 is closer to V2 generally, but it is similar to V1 in terms of Attack rate.

• Novel methodology in creating a realistic social contact network for a typical urban area in developing countries

• Detailed structure analysis reveal:– Generic properties for large scale social contact network– Region specific features are captured in the model

• Simulation study shows:– The epidemic dynamics of the region is strongly influenced by activity

pattern and demographic structure of local residents

• Comparison to a coarser network suggests:– A high resolution social contact network helps us make better public

health policy

Conclusions

END

Questions?

EXTRA SLIDES

Epidemic Simulations Setup

• Disease model Flu similar to H1N1 in 2009: assume R0=1.35, 1.40, 1.45, 1.60

(only the results when R0=1.35 are shown, but others are similar) SEIR model: heterogeneous incubation and infectious durations 10 random seeds every day

• Interventions Vaccination: implemented at the beginning of epidemic; compliance rate 25% Antiviral: implemented when 1% population are infectious; covers 50% population;

effective for 15 days School closure: implemented when 1% population are infectious; compliance rate 60%;

lasts for 21 days Work closure: implemented when 1% population are infectious; compliance rate 50%;

lasts for 21 days

• Total five configurations (including base case). Each configuration is simulated for 300 days and 30 replicates

Targeted layered containment strategies

• In network construction, we assign people to locations based on gravity model.• What if locations are assigned randomly?• We randomly switch two people’s locations, illustrated below:

• The location switch can be modeled as so called “generalized switch”:

• Such switches in people-location network can be used to understand the sensitivity to location assignment.

Sensitivity Test I: generalized switch

Sensitivity Test I (on Delhi-V2): Trivial Difference with Location Switch

• The sensitivity test of location switch shows that the mobility pattern may not be a significant factor that influences either the social contact structure or the epidemic outcome of the population.

– The same conclusion applies to the scenarios in V2 (figures below).

Sensitivity Test II (on Delhi-V2): Significant Impact by Varying Sublocation Size

• V2 contains more types of locations than V1. – w: work sublocation size– s: school sublocation size– c: college sublocation size– sp: shopping center sublocation size– o: other place sublocation size

• Nevertheless, the same conclusion as for V1 holds.

• We have run preliminary tests on the generated synthetic populations and networks of Delhi to examine the robustness of our new model.

• The first test involves switching locations of specific types of activities. • The second test involves varying the sublocation sizes in the sublocation models

which are used for generating networks from the synthetic populations. • Our tests suggest that, identifying appropriate models for people-people contacts

at sublocations is more important than finding appropriate models for activity-location assignments.

• As a part of the project, we have extended our network sensitivity methodology to understand the effects of network construction method.

Sensitivity Test: conclusion

• Population generationInput: Joint distribution of age and gender of the population in Delhi (from the India

census 2001)

Algorithm:– Normalize the counts in the joint distribution of age and gender into a joint

probability table– Create 13.85 million individuals one by one.

For each individual: Randomly select a cell c with the probability of each cell of the city.Create a person with the age and gender corresponding to the cell c.

End

Output: 13.85 million individuals are created, each individual is associated with disaggregate attributes of gender and age.

V1: synthetic population generation

V2: household distribution – a snapshot

• Households are distributed along real streets/community blocks.• V2 avoids to distribute households on rivers, lakes and green land etc. (V1 distribute them

uniformly within each 1(miles)*1(miles) block)

V2: the distribution of people in non-household locations

• Gravity Model: same as V1.• No people/locations are distributed over the Yamuna river.

• Same methodology as we did for US populations:Input: total # of households

Aggregate distribution of demographic properties from Census: hh size, householder’s age

Household micro-samplesOutput: Synthetic population with household structure. Each individual is assigned an age and gender.Algorithm:

1. Estimate joint distribution of household size and householder’s age: 1) construct a joint table of hh size and householder’s age: fill in # of samples for each cell2) multiply total # of households to distributions to calculate marginal totals for the table3) run IPF to get a convergent joint table4) normalize: divide counts in each cell with (total # of samples), it’s probability for each

cell.(illustrated in next slide)

2. create the synthetic households and population:1) randomly select a cell with the probability in joint table2) select a household sample h from all samples associated with that cell uniformly at

random3) create a synthetic household H, so that H has same members as h, each member in H has

same demographic attributes as those in h.4) repeat step 2.1-2.3, until # of synthetic households is equal to the total # of households

from Census.

V2: synthetic population creation method

IPF example

Row Adjustment   Column Adjustment  

Iteration 129.62 39.61 30.76 35 40 25

20 8.00 8.00 4.00 20.78 9.45 8.08 3.2530 8.57 10.71 10.71 29.65 10.13 10.82 8.7135 11.25 12.50 11.25 35.06 13.29 12.62 9.1415 1.80 8.40 4.80 14.51 2.13 8.48 3.90

Iteration 234.81 40.09 25.10 35 40 25

20 9.10 7.77 3.13 20.02 9.15 7.76 3.1230 10.25 10.95 8.81 30.00 10.30 10.92 8.7735 13.27 12.60 9.13 35.01 13.34 12.57 9.0915 2.20 8.77 4.03 14.98 2.21 8.75 4.02

Iteration 3: Finished34.99 40.00 25.00 35 40 25

20 9.14 7.75 3.11 20.00 9.14 7.75 3.1130 10.30 10.92 8.78 30.00 10.30 10.92 8.7735 13.34 12.57 9.09 35.00 13.34 12.57 9.0915 2.21 8.76 4.02 15.00 2.21 8.76 4.02

Row  Column

20 3530 4035 2515

Start35 40 25

20 6 6 330 8 10 1035 9 10 915 3 14 8

• Extract travel categories based on the socio-economic and demographic profile of the Thane sample (Adults) and school attendance statistics from UIS (students).

Adults: (i) zero trip maker (home all day) (ii) commuter (with work activity) (iii) non commuter (makes at least one trip but no work trips) (iv) college (only for those aged 18-21) Kids: (i) school (attends school) (ii) non school (does not attend school) (iii) zero trip maker (home all day)

• Thane contains trip start time distributions and trip time distributions for adult commuters and non commuters.

– Choose appropriate trips for each individual relevant to his/her respective commuter category (for example, a non worker A should not be assigned a home-work trip, let’s say A’s trips on the day are: home-shop and shop-home).– Sample alternately from trip start time distributions and trip duration distributions to generate time slots for each selected trip, with a

constraint that two symmetric trips take equal duration. (e.g, we sample for A: 2:00pm-2:20, home-shop; 3:40-4:00, shop-home)– Generate a sequence of activities between trips to fill in the 24 hours in the day.

(e.g, for A: 0:00am-2:00pm, home, 2:20pm-3:40pm, shop, 4:00-11:59pm, home)

• Thane survey statistics provide no particular information on school and college trip times and trip durations. As a result following assumptions were made regarding travel patterns for kids (age 0-17) and college attendees (aged 18-21):

– Kids aged 0-5 years are assigned same activities as an adult in the household.– Non school attendees are modeled as non commuters (i.e. non working adults).– Fixed daily schedules assigned to all school and college attendees.

e.g., College-goers attend college between 9:00 am and 3:00 pm. Remainder of the time is spent at home.

V2: Generating Activity Sequences based on Thane Survey