Waning Immunity and the Second Wave: Some Projections for SARS CoV 2

This paper offers projections of future transmission dynamics for SARS-CoV-2 in an SEIRS model in which immunity is waning over time. In a stylized optimal control setting calibrated to the USA, we show that the optimal social distancing policy is to reduce contact rates in the population for the first half year, and then to slightly relax these policies and switch to a permanent management of an endemic disease state. The optimal policy has three distinct features, namely mitigation, delay and non-eradication. We simulate how the optimal policy depends on how fast immunity wanes and on the infection fatality rate.