﻿ 具有饱和感染率的随机SIR传染病模型的性质分析

# 具有饱和感染率的随机SIR传染病模型的性质分析Qualitative Analysis of a Stochastic SIR Epidemic Model with Saturated Incidence Rates

Abstract: A stochastically mathematical model of a stochastic SIR epidemic model with saturated incidence rates is proposed and analyzed, setting that all the death rate and incident rate are similarly per-turbed by an independent Gaussian white noise. First the paper shows that the infective population and recovered individuals will tend to zero exponentially almost surely under some additional condition. In addition, a sufficient condition for the stationary distribution around the endemic infection equilibrium state of the corresponding deterministic model is derived and the solution is ergodic.

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