Optimal vaccination patterns in age-structured populations: Endemic case

We consider a simple age-structured SIR model with vaccination and separable mixing. We define costs for a vaccination strategy (number of vaccinations per time) and effect (reduction of prevalence of disease or reduction of the number of risk cases). We consider two optimization problems: to find the strategy with minimal costs at a given level for the effect, and also to find the strategy with maximal effect at given costs. It turns out that there is an optimal strategy that is nonzero only in at most three age classes, i.e., consists of a sum of at most three delta-peaks.