1. The Importance of Detail: Sensitivity of Household Secondary Attack Rate and Intervention Efficacy to Household Contact Structure A. Marathe, B. Lewis, J. Chen and S. Eubank VBI at Virginia Tech Modeling for Public Health Action Atlanta Dec. 10, 2010 Network Dynamics and Simulation Science Laboratory

2. Detail is important in models of complex systems Point estimates vs distributional estimates Mean behavior not representative in nonlinear systems Structure of interactions is as important as the nature of the interactions Particularly for targeted interventions with limited resources in social systems, where information, trust and access to resources are inhomogeneous.

3. Importance of Detail is a Double-edged Sword The bad news: extra burden on modelers –Providing timely advice is difficult –Requires preparation (developing models ahead of time) –Requires generalization (avoiding stovepipes) The good news: effects of PH actions may also be amplified –Small, carefully targeted action may have significant effects E.g. herd immunity –Actions in seemingly unrelated areas may be possible E.g. social network approaches to obesity and tobacco use

4. Realizing the possibility relies on mathematical modeling Controlled, longitudinal studies are impossible, expensive, or unethical Intuitive, mental models based on experience are not amenable to rigorous testing Decisions often involve comparing apples to oranges: E.g. relative cost/benefit of closing schools to a vaccination campaign

5. This talk: modeling in-home care-giving Through policy or overwhelming demand, care-giving outside clinical care settings will be widespread in a severe pandemic. What effect do different care-giving strategies have? What happens if models don’t account for different strategies?

6. Modeling contagion person-person through a network The model has two essential features: 1.Opportunities for transmission, represented as a dynamic network 2.Probabilities for transmission The transmission model is (overly?) simple, but it can be calibrated to fit historical data, e.g. estimates of household secondary attack rate. Importantly, the basic reproductive number R 0 is not a parameter, but is measurable from simulations of the model.

7. += Opportunities for transmission Transmission rates Epidemic model

8. Consider 2 extreme care-giving strategies 1.Each person retains opportunities to infect everyone else: a “complete” network 2.Symptomatic people are isolated from the household, except for a single care-giver: a “star” network

9. Estimating the magnitude of effect is important Which strategy is typically employed in which households? Is a star strategy common enough to warrant providing care-givers prophylaxis? Are historical estimates of R 0 significantly biased by this effect? Is it common enough to throw off estimates of effects of home care- giver education? How do effects depend on the person-person transmission rate? How do effects depend on local demographics?

10. Regions differ in household demographics AgeMiamiSeattle 0 - 477 5 - 181520 19 - 646563 65+1310 HH sizeMiamiSeattle 1811 2 – 33846 4 or more5443

11. Experiment Calibrate transmission rates separately for Miami and Seattle to produce overall infection attack rates of 20% (“low”) and 60% (“high”) for both, assuming the “complete” household networks Evaluate the overall attack rate for each transmission rate and each city under both the “complete” and “star” network assumptions, with no interventions, using 100 stochastic simulation runs for each. Evaluate the household secondary attack rate and its dependence on household size.

12. Calibration