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.

In this paper, we present an SIRS (Susceptible, Infective, Recovered, Susceptible) epidemic
model with a saturated incidence rate and disease causing death in a population of varying
size. We define a parameter ℜ0* from which a study of stability is made. In the deterministic
case, we discuss the existence of an endemic equilibria and prove the global stability of the
disease-free equilibrium. By introducing a perturbation in the contact rate through a white
noise, we consider a stochastic version. We prove the existence of a global positive solution …