Abstract
This paper considers a stochastic SIS model with saturated incidence rate. We investigate the existence and uniqueness of the positive solution to the system, and we show the condition for the infectious individuals to be extinct. Moreover, we prove that the system has the ergodic property and derive the expression for its invariant density. The simulation results are illustrated finally.
Highlights
Epidemic models have been studied by many researchers due to their great influence on human life
6 Conclusion In this paper, we have considered the features of a SIS epidemic system with the effect of environmental white noise
Theorems . , . , and . show that the disease will be extinct if Rs ≤, and the disease will be epidemic if Rs >
Summary
Epidemic models have been studied by many researchers due to their great influence on human life. ) is as follows: (i) The disease-free equilibrium E = (N, ) is globally asymptotically stable if Into epidemic models, where α is a positive constant, βI Since S(t) + I(t) = N , studying the following equation is enough: β(N – I(t))I(t) Throughout this paper, let ( , F , P) be a complete probability space with a filtration {Ft}t≥ satisfying the usual conditions (i.e. it is increasing and right continuous while F contains all P-null sets) and B(t) be a scalar Brownian motion defined on the probability space.
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