This paper analyzes a simple model of infectious disease where the incentives for individuals to reduce risks through endogenous social distancing take straightforward cost-benefit form. Since disease is transmitted through social interactions, the threat of spread of infection poses a collective action problem. Policy interventions such as lockdowns, testing, and mask-wearing serve, in part, as substitutes for social distancing. Provision of a vaccination is the only intervention that unambiguously reduces both the peak infection level and the herd immunity level of infection. Adoption of vaccination remains limited in a decentralized equilibrium, with resulting reproductive rate of disease Rt > 1 at the conclusion of vaccination. Vaccine mandates yield increases in vaccination rates and corresponding reductions in future infection rates but do not increase expected payoffs to individuals.
Avery, Christopher. "A Simple Model of Social Distancing and Vaccination." HKS Faculty Research Working Paper Series RWP21-030, November 2021.