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.
