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 n nIncludes: Distribution of medicines and health care Command / control for isolation, quarantine, emergency response Monitoring / outbreak detection n nOperates on mobile people No mobility  no consequence management problem Disease spread intricately connected to mobility People defined as users of transportation infrastructure n nInteractions 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 15 age Over age 55 Susceptible Infected Recovered Mixing rate Reproductive number

Individual-Based Models Complement Traditional Epidemiological Models Individual-Based Model: Individuals carry many demographics Individual contact rates estimated independently Reproductive number emerges from transmission

Top Down Structuring is Ambiguous Homogenous Isotropic ?... ~ 2~ 2~ 2~ 2 N2 alternative networks

Why Instantiate Social Networks? N vertices -> ~ 2 (N 2 ) 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 betweenness

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 map Family’s activities Contact matrix for entire population Epidemic snapshotEpidemic curves

A Typical Family’s Day Carpool Home WorkLunchWork Carpool 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 Home

Representing contacts – adjacency matrix Contact matrix for entire population (at 10 AM)

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  1)

Representing Contact Patterns – Social Network Graph Contacts among the household’s contacts (within distance 1)

Representing Contact Patterns – Social Network Graph Contacts’ contacts (distance 1  2)

Representing Contact Patterns – Social Network Graph Contacts among the contacts’ contacts (within distance 2)

distance 2  3

Within distance 3

Local network to distance 3

(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 at a 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 (# dead by day 100) / (# attacked)

Example 1: overall results (# dead by day 100) / (# attacked)

Example 1: overall results (# dead by day 100) / (# attacked)

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’ contactsInfecteds’ 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 solutions Marathe, 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