A Tale of Two Doses: Model Identification and Optimal Vaccination for COVID-19

We address the model identification and the computation of optimal vaccination policies for the coronavirus disease 2019 (COVID-19). We consider a stochastic Susceptible- Infected-Removed (SIR) model that captures the effect of multiple vaccine treatments, each requiring a different number of doses and providing different levels of protection against the disease. We show that the inclusion of vaccination data enables the estimation of the state of the model and key model parameters that are otherwise not identifiable. This estimates can, in turn, be used to design strategic approaches to vaccination that aim at minimizing the number of deaths and the economic cost of the disease. We illustrate these results with numerical examples.