Modeling for Science andPublic Health, Part 2

NAGMS CouncilJanuary 25, 2013

Stephen EubankVirginia Bioinformatics Institute

Virginia Tech

Infectious disease modeling has changed Then: coupled rate equations (SEIR)

– Ross, MacDonald, Kermack, McKendrick, Reed, Frost– nonlinear response, herd immunity & R0

– results like this:

Infectious disease modeling has changed Now: systems science perspective

– simulations with diverse, interacting parts– society, behavior, environment, demographics– results like this:

Networks represent systems of interacting entities

Vertices -> entitiesEdges -> interactions

Interactions change entities’ internal states and network structure changes, producing system-level dynamics.

Networks represent infectious disease epidemiology

Vertices -> peopleEdges -> proximity

Interactions change peoples’ health/beliefs/behavior and contacts change, producing epidemic dynamics.

Targeted interventions can berepresented as network changes

Vaccination

Messaging

Sequestration

Isolation

Vertex / edge choices represent many systems

0-5 year olds

school-age

adults

co-location

Vertex / edge choices represent many systems

vectors

livestock

humans

biting behavior

Vertex / edge choices lead to many* systems

female heterosexualnon injecting drug user

male bisexual injecting drug user

…

needle sharing,unprotected sex

* cf Hethcote, “A thousand and one epidemic models”, Frontiers in Math. Bio. (1994)

A complete solution is impossible

It would require 1.5 PB for 32 people with states (S,I,R)

(kN possibilities): the network correlates entities’ states.

Alice Bob Carol David Ellen probability of this configurationof states (today)

S S S R S 0.002

I S R R S 0.013

I I S S S 0.004

S I R S R 0.108

I I I R S 0.006

S R I S R 0.030

I S R R S 0.001

R R I S S 0.092

R I R I S 0.006

Agent-basedmodels

Compartmental models

Reaction-diffusion models

Compartmental models• emphasize aggregate, population outcomes• assume entities are indistinguishable &

averages are representative• produce equations of state

Reaction-diffusion models

• emphasize network structure• assume fixed detailed network• are “equation-free”

subgraph selection transmission tree reconstruction

Agent-based models•emphasize behavior•assume details are known•simulate a few instances

work workshoplunchcarpool

daycare

home home

bus school

car

Different models are appropriate for different questions

It’s better to have an approximate answer to the right question than an exact answer to the wrong question.

- John Tukey

Leveraging transdisciplinary insights

• Physics:– How do transition properties depend on network topology?– Scale-free networks only have an epidemic phase

• Chemistry:– How do aggregate properties of well-mixed systems

emerge?– coupled rate equations (structured compartmental model)

• Discrete math, combinatorics, computer science:– How can I approximate solutions efficiently?– feasibility of solving/approximating classes of problems

Regional variations matter …

… and depend on aggregate demographics

% attack rate

School contact networks matter …

H. Xia, J. Chen, M. Marathe, H. Mortveit (2011) Synthesis and refinement of detailed subnetworks in a social contact network for epidemic simulations. Proc. Int’l Conf. on Social Computing, Behavioral modeling and Prediction, College Park, Maryland.

… even though they affect only details

DegreeShortest Paths

Clustering

Household caregiving behavior matters…

A Marathe, B Lewis, J Chen, S Eubank Sensitivity of Household Transmission to Household Contact Structure and Size. PLOS One, 6(8): e22461

… but is hard to observe

Not “assume a spherical cow …”

What to expect from the new infectious disease models

Expect simplificationsthat reflect Public Health understanding, not mathematical / computational convenience

MODEL

Not “turn to page 79 of your textbooks …”

Scientific modeling is an art and a research program. Expect creativity,not pat solutions.

What to expect from the new infectious disease models