Optimality of Vaccination for Prevalence-Constrained SIRS Epidemics

The aim of the present paper is to investigate the optimal vaccination policies with prevalence restrictions in an SIRS demographic model. We provide a well-posedness result for the system and give a thorough description of safety zones (immunity and feasible) when intensive care units (ICU) restrictions are enforced on the prevalence. Using Pontryagin’s principle for state-constrained dynamics we show that the optimal vaccination policy is of bang–bang type and give further specifics on the precise structure. The paper is intended as a counter-part to Avram et al. (Appl Math Comput 418:126816, 2022) where non-pharmaceutical interventions have been considered.