Dynamics of an SIS Epidemic Model with Double Epidemic Hypothesis

In this paper we have proposed an SIS epidemic model with saturated incidence and double epidemic hypothesis. We analyzed the stability of equilibrium of the deterministic system by the threshold value and acquire the condition for elimination of the epidemic diseases. In this study the environment variability is characterised by white noise. The SIS Stochastic epidemic model is introduced from deterministic epidemic framework. The mean square and exponential stability for the stochastic model is determined and the significant differences between the result of deterministic and stochastic model is illustrated by numerical simulations with the set of hypothetical data.