Optimal control and analysis of a stochastic SEIR epidemic model with nonlinear incidence and treatment

In this paper, we represented the optimal control and dynamics of a stochastic SEIR epidemic model with nonlinear incidence and treatment rate. By using the Lyapunov function method, the existence and uniqueness of the global positive solution of the model were proved. The dynamic analysis of the stochastic model was studied and we found that the model has an ergodic stationary distribution when $R_0^s>1$. The disease was extinct when $R_0^e<1$. The optimal solution of the disease was obtained by using the stochastic control theory. The numerical simulation of our conclusion was carried out. The results showed that the disease decreased with the increase of the control variables.