Closed-Form Solutions for Optimal Social Distancing in a SIR Model of Covid-19 Suppression

I present a stylized suspected-infected-recovered (SIR) model of Covid-19, with symptomatic versus asymptomatic patients, and social distancing intervention. The optimal suppress strategy has low-infection rates, enabling assumptions that support closed-form solutions. The model predicts high costs of social distancing in comparison to health costs of the disease; it separates public versus private benefits of social distancing, and determines the required level of group immunity for relaxing social distance intervention. I extend the model with heterogeneous population for preferences over social contacts, health costs, and transmission. Heterogeneity in transmission intensity offers most opportunities for reduced costs under a differentiated social distancing policy.