Optimizing vaccination strategies in an age structured SIR model

We present a modeling framework based on a structured SIR model where different vaccination strategies can be tested and compared. Vaccinations can be dosed at prescribed ages or at prescribed times to prescribed portions of the susceptible population. Different choices of these prescriptions lead to entirely different evolutions of the disease. Once suitable "costs" are introduced, it is natural to seek, correspondingly, the "best" vaccination strategies. Rigorous results ensure the Lipschitz continuous dependence of various reasonable costs on the control parameters, thus ensuring the existence of optimal controls and suggesting their search, for instance, by means of the steepest descent method.