Modeling for Science and Public Health, Part 2 NAGMS Council January 25, 2013 Stephen Eubank Virginia Bioinformatics Institute Virginia Tech

Infectious disease modeling has changed Then: coupled rate equations (SEIR) – Ross, MacDonald, Kermack, McKendrick, Reed, Frost – nonlinear response, herd immunity & R 0 – 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 -> entities Edges -> interactions Interactions change entities’ internal states and network structure changes, producing system-level dynamics.

Networks represent infectious disease epidemiology Vertices -> people Edges -> proximity Interactions change peoples’ health/beliefs/behavior and contacts change, producing epidemic dynamics.

Targeted interventions can be represented 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 heterosexual non 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) (k N possibilities): the network correlates entities’ states. AliceBobCarolDavidEllenprobability of this configuration of states (today) SSSRS0.002 ISRRS0.013 IISSS0.004 SIRSR0.108 IIIRS0.006 SRISR0.030 ISRRS0.001 RRISS0.092 RIRIS0.006

Agent-based models 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 shop lunch carpool daycare 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 Degree Shortest 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 simplifications that 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