Global Dynamics of a Generalized SIRS Epidemic Model with Constant Immigration

Abstract EN

In this paper, we discuss the global dynamics of a general susceptible-infected-recovered-susceptible (SIRS) epidemic model.

By using LaSalle’s invariance principle and Lyapunov direct method, the global stability of equilibria is completely established.

If there is no input of infectious individuals, the dynamical behaviors completely depend on the basic reproduction number.

If there exists input of infectious individuals, the unique equilibrium of model is endemic equilibrium and is globally asymptotically stable.

Once one place has imported a disease case, then it may become outbreak after that.

Numerical simulations are presented to expound and complement our theoretical conclusions.