Waning Immunity and the Second Wave

In this paper, Chryssi Giannitsarou, Stephen Kissler, and Flavio Toxvaerd, consider the optimal social distancing policy in an SEIRS model of the COVID-19 epidemic in which immunity wanes over time. We calibrate the model to the US and consider the effects of different waning periods for the dynamics of the disease and the path of optimal control. We show that the possibility of waning immunity qualitatively changes the trajectory of social distancing even at early stages of the epidemic and that the return to susceptibility creates the potential for a second wave of infection.