modeling for science and public health, part 2 nagms council january 25, 2013 stephen eubank...
TRANSCRIPT
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Modeling for Science andPublic Health, Part 2
NAGMS CouncilJanuary 25, 2013
Stephen EubankVirginia Bioinformatics Institute
Virginia Tech
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Infectious disease modeling has changed Then: coupled rate equations (SEIR)
– Ross, MacDonald, Kermack, McKendrick, Reed, Frost– nonlinear response, herd immunity & R0
– results like this:
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Infectious disease modeling has changed Now: systems science perspective
– simulations with diverse, interacting parts– society, behavior, environment, demographics– results like this:
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Networks represent systems of interacting entities
Vertices -> entitiesEdges -> interactions
Interactions change entities’ internal states and network structure changes, producing system-level dynamics.
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Networks represent infectious disease epidemiology
Vertices -> peopleEdges -> proximity
Interactions change peoples’ health/beliefs/behavior and contacts change, producing epidemic dynamics.
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Targeted interventions can berepresented as network changes
Vaccination
Messaging
Sequestration
Isolation
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Vertex / edge choices represent many systems
0-5 year olds
school-age
adults
co-location
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Vertex / edge choices represent many systems
vectors
livestock
humans
biting behavior
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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)
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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
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Agent-basedmodels
Compartmental models
Reaction-diffusion models
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Compartmental models• emphasize aggregate, population outcomes• assume entities are indistinguishable &
averages are representative• produce equations of state
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Reaction-diffusion models
• emphasize network structure• assume fixed detailed network• are “equation-free”
subgraph selection transmission tree reconstruction
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Agent-based models•emphasize behavior•assume details are known•simulate a few instances
work workshoplunchcarpool
daycare
home home
bus school
car
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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
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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
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Regional variations matter …
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… and depend on aggregate demographics
% attack rate
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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.
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… even though they affect only details
DegreeShortest Paths
Clustering
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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
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… but is hard to observe
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Not “assume a spherical cow …”
What to expect from the new infectious disease models
Expect simplificationsthat reflect Public Health understanding, not mathematical / computational convenience
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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