Disease spread coupled with evolutionary social distancing dynamics can lead to growing oscillations.

If the public's adherence to social distance measures remained steady during an outbreak, the number of cases would have a single peak followed by a sharp decline according to standard epidemiological models. Nonetheless, during COVID-19 the initial rise and fall in the number of cases followed new waves of cases in many localities. In this paper, we explore a standard susceptible-exposed-infected-recovered (SEIR) epidemiological model coupled with an individual behavior response model that modulates the contact rate. A game with payoffs determined by the state of the disease captures the public's incentive to comply with the social distancing measures. We use replicator dynamics to model the response to changes in incentives. Using SEIR dynamics coupled with replicator dynamics, we identify a set of dynamics that can lead to growing oscillations in the number of cases until herd immunity is reached. According to the dynamics, an increase in the number of infected individuals changes the payoffs such that the public's cooperation level eventually increases. Increased cooperation levels is followed by a reduced number of cases in the community, which then reduces the public's incentive to cooperate. The decrease in the cooperation levels causes the number of cases to rise again. These waves correspond to cycles between cooperation and defection behavior, and the rise and fall of the number of the infected individuals. The proposed model also provides a proper tool to study the effects of the public health policies that aim to curb the growth in number of cases by providing incentives to cooperate.