Optimal Vaccination Strategy under Saturated Treatment using the Stochastic SIR Model

Abstract

This paper is concerned with the control strategy by vaccination of the infectious disease spreadin the populations consisting of the susceptible, the infected and the recovered (SIR). In the realisticspread of the infectious disease, changes in the environment and the weather cause some kinds ofrandom fluctuations in the infection and the recovery rates, etc. Moreover, medical facilities havegenerally the maximal capacity for treatment of diseases. Taking these facts into consideration, wepropose the stochastic infectious model with vaccination and saturated treatment, and we considerthe stochastic optimal vaccination problem for the SIR model with saturated treatment using thestochastic maximum principle and the four-step scheme. We construct a feasible optimal vaccinationsystem. By numerical simulations, we validate the efficacy of the optimal vaccination strategy.