Dynamics of a Deterministic and Stochastic Susceptible-Exposed-Infectious-Recovered Epidemic Model

Abstract

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.