Equilibria of an Epidemic Game with Linear Social Distancing Cost

Epidemics can put people’s health at risk, and people often change their behaviors during epidemics to increase their social distance from others and thus to reduce their risk of infection. Since behavior changes can be costly, we would like to know the optimal social distancing behavior. But the benefits of changes in behavior de-pend on the course of the epidemic, which themselves depend on people’s behaviors. Differential population game theory provides one approach resolving this interde-pendence. This paper contains the analysis of a special case of the differential SIR epidemic population game with social distancing when the relative infection rate is linear, with a zero lower bound. Complete closed-form results are obtained in the infinite-horizon case. Constructions are also provided for the finite-horizon case when universal vaccination occurs after a fixed delay, providing upper bounds on the window of opportunity for vaccine deployment. 1