National Infrastructure Simulation & Analysis Center NISAC PUBLIC HEALTH SECTOR:

Disease Outbreak Consequence Management

Stephen Eubank

Los Alamos National Laboratory

April 2003

Interdependent Infrastructure Simulations

Public Health Infrastructure

Includes:• Distribution of medicines and health care• Command / control for isolation, quarantine, emergency response• Monitoring / outbreak detection

Operates on mobile people

• No mobility no consequence management problem

• Disease spread intricately connected to mobility

• People defined as users of transportation infrastructure

Interactions with other sectors• Food or water-borne disease• Demand for distribution of basic life-support (food, water, energy)• Robust against disease susceptible to natural disaster ??

Simulate outbreak to evaluate objective (cost) function

• Path of outbreak determined by individuals’ use of infrastructure

• Public Health controls behavior and response of individuals

• Interaction with other sectors mediated by individuals

Model complex interactions between aggregate systems

OR

Simulate much simpler interactions between many individuals

Individual-Based Models Complement Traditional Epidemiological Models

Traditional rate equations model subpopulations:

• Subpopulation based on a few demographics

• Subpopulation mixing rates unknown

• Reproductive number not directly observable

Under age 15age 15 - 55

Over age 55

Susceptible

InfectedRecovered

Mixing rate

Reproductivenumber

Individual-Based Models Complement Traditional Epidemiological Models

Individual-Based Model:

• Individuals carry many demographics

• Individual contact rates estimated independently

• Reproductive number emerges from transmission

Age 26 26 7

Income $27k $16k $0

Status worker worker student

Automobile

Top Down Structuring is Ambiguous

Homogenous

Isotropic

??

. . .. . . ~~ 22NN 22 alternative

networks

Why Instantiate Social Networks?

• N vertices -> ~ 2(N2) graphs(non-identical people -> few symmetries)

• E edges -> ~ N(2E) graphs

• Degree distribution -> ?? graphs

• Clustering coefficient -> ?? graphs

• What additional constraints -> graphs equivalent w.r.t. epidemics?

Measures of Centrality

Same degree distribution (green vertices are degree 4, orange degree 1)

Different assortative mixing by degree

High High betweennessbetweenness

Gaps in existing technology

• Need novel combination of scale and resolution– Ackerman, Halloran, Koopman:

individual resolution, only ~1000 people

– Murray, Hethcote, Kaplan, many others:mixing in infinitely large populations, no resolution

– EpiSims: millions of individual people interacting with other sectors

• Initial stages crucial for response– Individual based simulation only tool focused there

Individual-based epidemiology: a road mapFamily’s activities Contact matrix for entire population

Epidemic snapshot Epidemic curves

WORK WORK

SHOP SHOP

SCHOOL SCHOOL SCHOOL SCHOOL

DAYCAREDAYCARE

SCHOOL SCHOOL SCHOOL SCHOOL

SCHOOL SCHOOL SCHOOL SCHOOL

SCHOOL SCHOOL SCHOOL SCHOOLSCHOOl SCHOOL SCHOOL SCHOOL

WORK WORKWORK WORK

SHOP SHOPSHOP SHOP

DAYCARE DAYCAREDAYCARE DAYCARE

A Typical Family’s Day

Carpool

HomeHome

Work Lunch WorkCarpool

Bus

Shopping

Car

Daycare

Car

School

time

Bus

Others Use the Same Locations

Time Slice of a Typical Family’s Day

Who’s in contact doing what at 10 AM?

Work

Shopping

Daycare

School

A Scared Family’s Possible Day

HomeHome

Representing Contact Patterns – Social Network Graph

Household of 4 (distance 0)

Representing Contact Patterns – Social Network Graph

Contacts of people in the household (distance 0 Contacts of people in the household (distance 0 1) 1)

Representing Contact Patterns – Social Network Graph

Contacts among the household’s contacts (within distance 1)Contacts among the household’s contacts (within distance 1)

Representing Contact Patterns – Social Network Graph

Contacts’ contacts (distance 1 Contacts’ contacts (distance 1 2) 2)

Representing Contact Patterns – Social Network Graph

Contacts among the contacts’ contacts (within distance 2)Contacts among the contacts’ contacts (within distance 2)

distance 2 distance 2 3 3

Within distance 3Within distance 3

Local network to Local network to distance 3distance 3

Local network to Local network to distance 3distance 3(Side view)(Side view)

Disease Progression Model

Transmission Implementation I

If contagious, a person sheds into environment at a rate proportional to his/her load.

Each person absorbs from environment ata different rate proportional to its contamination.

environment

Transmission Implementation II

Stochastic transmission from contagious to susceptibles in the same location

How Technology Answers Specific Questions

1. Assess mitigation strategies (OHS study)

2. Identify critical path for disease spread (OHS request)

3. Determine optimal sensor deployment

4. Support tabletop exercises

5. Evaluate logistical requirements for responders

6. Develop requirements for effective vaccine

7. Decision support for medical surveillance

Example 1: mitigation strategies

• Attacks on complementary demographics– Shopping mall

– University

• Responses– Baseline: no response

– Mass vaccination

– Targeted vaccination & isolation

– Targeted, but with limited resources

• Implementation delay: 4, 7, 10 days

• Policy: self-imposed isolation (withdrawal to the home)– Before becoming infectious (“EARLY”)

– 12-24 hours after becoming infectious (“LATE”)

– “NEVER”

Example 1: targeted vax + isolation

Example 1: targeted, limited resources

Example 1: overall results(#

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day

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Example 1: overall results(#

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Example 1: overall results(#

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Example 2: critical path

• Study properties of social network directly

• Study random graphs resembling social networks

• Simulate to find disease mixing rates

Example 2: contact pattern variability

Strangers’ contacts Infecteds’ contacts

Example 2: metrics for social networks

• Vertex degree, clustering too local

• Other classical graph-theoretical measures of centrality

• Betweenness “too” global to compute efficiently (but sampling may give provably good approximations)

• Finite-radius betweenness?– e.g. how many paths of length d use a particular edge

– reflects importance of incubation period

Example 2: mixing rate experimental design

• Infect samples of a very specific demographic group

– E.g. households with at least 3 children under 18 and 1 child between 5 and 10

– Not intended to model attack or natural introduction

– Pick groups at extremes of gregariousness

• Estimate demographics of each cohort (disease generation)

• Compare to demographics of entire population

Example 3: optimal sensor deployment

Suppose we have a bio-sensor that detects infected people.

• How many sensors must be deployed to cover a fixed fraction of the population?

• Where?

• Who is covered?

• Evaluate cost/benefit of sensor refinements

Algorithms for coverage

• Dominating set

– on bipartite graph (locations and people)

– ~2 million vertices, ~10 million edges

– but with little overlap between high degree locations

• Fast, very good approximate solutionsMarathe, Wang, Vullikanti, Ravindra

Example 4: Tabletop exercises

• Compare with scripted casualties as in Dark Winter

• Reacts to decisions

• Connects to evacuation planning and other sectors addressed in most exercises

Example 5: responder logistics

• Resources required to implement response

• Demand placed on resources by sick, worried well

• Demand placed on other infrastructures– Public health

– Transportation (evacuation, service delivery)

– Communication (phone networks overloaded)

– Power, water, food distribution

Example 6: vaccine design

• Postulate vaccine properties:– Contra-indications

– Communicability of vaccine induced illness

– Time between vaccination and protection

– Efficacy at preventing infection / transmission

• Simulate “trials” to establish consequences:– Disease casualties

– Direct casualties of vaccination

– Indirect casualties of vaccination

– Interruption of social enterprise

Example 7: medical surveillance

• Anomaly in number of people presenting certain symptoms provokes suspicion of disease outbreak

• Simulation estimates population’s health state over near future under hypothesis

• Verify against observations

Possible Future Directions

• Licensing software, partnering, outreach

• Generic / parameterized cities

• Software development

– User interface

– More flexible health characteristics generator

– Multiple days / seasonality / weekends

– Multiple co-circulating (interacting) diseases

– Simulation state manipulation

– Additional exogenous events