THE OPTIMAL CONTROL OF THE STOCHASTIC SIV EPIDEMIC MODEL WITH INDIVIDUAL INTERACTIONS

In this paper, based on the mean field theory, we investigate a reaction diffusion stochastic susceptible-infected-vaccinated (SIV) epidemic model with individual interactions, and focus on the optimal control problem of the model. Within the framework of the Stieltjes integral and using the Martingale representation theorem, we show the existence and uniqueness of solution related to a reaction diffusion stochastic SIV epidemic system with impulse effects and Lévy noise. Furthermore, the sufficient and necessary conditions of optimal control for the stochastic SIV epidemic model under appropriate assumptions are obtained. The proof of our main results is based on Ekeland’s variational principle and some estimates of the state variables and adjoint processes. Ultimately, numerical examples are presented to illustrate the effectiveness of theoretical results.