Journal
BULLETIN OF MATHEMATICAL BIOLOGY
Volume 75, Issue 10, Pages 1961-1984Publisher
SPRINGER
DOI: 10.1007/s11538-013-9879-5
Keywords
Epidemiological games; Social distancing; SIR; Differential population game
Categories
Funding
- NSF [DMS-0920822]
- NIH [PAR-08-224]
- Bill and Melinda Gates Foundation [49276]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0920822] Funding Source: National Science Foundation
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Around the world, infectious disease epidemics continue to threaten people's health. When epidemics strike, we often respond by changing our behaviors to reduce our risk of infection. This response is sometimes called social distancing. Since behavior changes can be costly, we would like to know the optimal social distancing behavior. But the benefits of changes in behavior depend on the course of the epidemic, which itself depends on our behaviors. Differential population game theory provides a method for resolving this circular dependence. Here, I present the analysis of a special case of the differential SIR epidemic population game with social distancing when the relative infection rate is linear, but bounded below by zero. Equilibrium solutions are constructed in closed-form for an open-ended epidemic. Constructions are also provided for epidemics that are stopped by the deployment of a vaccination that becomes available a fixed-time after the start of the epidemic. This can be used to anticipate a window of opportunity during which mass vaccination can significantly reduce the cost of an epidemic.
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