Abstract
The purpose of this paper is to propose the stochastic infectious model and to construct the optimal vaccination strategy to control the infectious disease spread. In the realistic spread of the infectious disease, environmental change and individual difference cause some kinds of random fluctuations in the model parameters. Especially, we consider the random fluctuation in the recovery rate. Moreover, focusing on the case where the number of infectives is very high, we employ the nonlinear incidence rate. We propose the stochastic infectious model with the nonlinear incidence rate. In the optimal vaccination problem, we construct the optimal vaccination system using the stochastic maximum principle (SMP). In order to solve the forward-backward stochastic differential equation in the SMP, we apply the four-step scheme and verify the efficiency of the proposed vaccination strategy through the numerical simulations.
