(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
We investigate a susceptible-exposed-infectious-recovered (SEIR) epidemic model with asymptomatic infective individuals. First, we formulate a deterministic model, and give the basic reproduction number R_0. We show that the disease is persistent, if R_0 > 1, and it is extinct, if R_0 < 1. Then, we formulate a stochastic version of the deterministic model. By constructing suitable stochastic Lyapunov functions, we establish sufficient criteria for the extinction and the existence of ergodic stationary distribution to the model. As a case, we study the COVID-19 transmission in Wuhan, China, and perform some sensitivity analysis. Our numerical simulations are carried out to illustrate the analytic results.