Abstract
This paper is concerned with the control strategy by vaccination of the infectious disease spread in the populations consisting of the susceptible, the infected and the recovered (SIR). In the realistic spread of the infectious disease, changes in the environment and the weather cause some kinds of random fluctuations in the infection and the recovery rates, etc. Moreover, medical facilities have generally the maximal capacity for treatment of diseases. Taking these facts into consideration, we propose the stochastic infectious model with vaccination and saturated treatment, and we consider the stochastic optimal vaccination problem for the SIR model with saturated treatment using the stochastic maximum principle and the four-step scheme.
