  We study the interplay between epidemic dynamics and human decision making
for epidemics that involve reinfection risk; in particular, the
susceptible-infected-susceptible (SIS) and the
susceptible-infected-recovered-infected (SIRI) epidemic models. In the proposed
game-theoretic setting, individuals choose whether to adopt protection or not
based on the trade-off between the cost of adopting protection and the risk of
infection; the latter depends on the current prevalence of the epidemic and the
fraction of individuals who adopt protection in the entire population. We
define the coupled epidemic-behavioral dynamics by modeling the evolution of
individual protection adoption behavior according to the replicator dynamics.
For the SIS epidemic, we fully characterize the equilibria and their stability
properties. We further analyze the coupled dynamics under timescale separation
when individual behavior evolves faster than the epidemic, and characterize the
equilibria of the resulting discontinuous hybrid dynamical system for both SIS
and SIRI models. Numerical results illustrate how the coupled dynamics exhibits
oscillatory behavior and convergence to sliding mode solutions under suitable
parameter regimes.
