Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model

Abstract

We present in this paper an SIRS epidemic model with saturated incidence rate and disease-inflicted mortality. The Global stability of the endemic equilibrium state is proved by constructing a Lyapunov function. For the stochastic version, the global existence and positivity of the solution is showed, and the global stability in probability and pth moment of the system is proved under suitable conditions on the intensity of the white noise perturbation.

Keywords

• epidemic model,
• Lypunov function
• Ito’s formula
• global stability
• moment exponential stability