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 15
age 15 - 55
Reproductive
number
Susceptible
Mixing rate
Infected
Recovered
Over age 55
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
?
...
N 2 alternative
~2
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 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
WORK
WORK
SHOP
SHOP
SCHOOL SCHOOL SCHOOL SCHOOL
DAYCARE DAYCARE
SCHOOL
SCHOOL SCHOOL SCHOOL
SCHOOL
SCHOOL
SCHOOL
SCHOOl
SCHOOL SCHOOL
SCHOOL
SCHOOL SCHOOL SCHOOL
WORK
WORK
SCHOOL SCHOOL
WORK
WORK
SHOP
SHOP
SHOP
SHOP
DAYCARE
DAYCARE
Epidemic snapshot
Epidemic curves
DAYCARE
DAYCARE
A Typical Family’s Day
Work
Carpool
Lunch
Work
Carpool
Shopping
Home
Car
Home
Car
Daycare
Bus
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
Home
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
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.
environment
Each person absorbs from environment at
a different rate proportional to its contamination.
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
(# dead by day 100) / (# attacked)
Example 1: overall results
(# dead by day 100) / (# attacked)
Example 1: overall results
(# dead by day 100) / (# attacked)
Example 1: overall results
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 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