One of the most urgent questions in mathematical epidemiology is how to use control measures in an optimal way. We investigate the effect and effort of vaccination rates within the framework of age structured endemic models. These vaccination rates are not assumed to depend on time but on age. Also for the solution of the endemic model we do not consider time but assume the solution to stay in an equilibrium. The shape of this equilibrium will depend on the vaccination rate.
Most literature is concerned with the uninfected equilibrium.
All that can be done is to minimize the harmful effects of the disease. For example, in the case of rubella, the aim is to protect pregnant women. In this talk, we focus on endemic equilibria. We define the effect of a vaccination strategy as the reduction of the number of risk cases due to the infection per time interval. The effort of the vaccination strategy is defined as the number of vaccinations per time interval.