Dynamics of a Deterministic and Stochastic Susceptible-Exposed-Infectious-Recovered Epidemic Model (Journal of Nonlinear Modeling and Analysis, 2024)
We investigate a susceptible-exposed-infectious-recovered (SEIR)epidemic model with asymptomatic infective individuals. First, we formulatea deterministic model, and give the basic reproduction number $R_0.$ We showthat 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 constructingsuitable stochastic Lyapunov functions, we establish sufficient criteria for theextinction 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 toillustrate the analytic results.