  SIR models, also with age structure, can be used to describe the evolution of
an infective disease. A vaccination campaign influences this dynamics
immunizing part of the susceptible individuals, essentially turning them into
recovered individuals. We assume that vaccinations are dosed at prescribed
times or ages which introduce discontinuities in the evolutions of the S and R
populations. It is then natural to seek the 'best' vaccination strategies in
terms of costs and/or effectiveness. This paper provides the basic well
posedness and stability results on the SIR model with vaccination campaigns,
thus ensuring the existence of optimal dosing strategies.
