Abstract
In this paper, a stochastic SIS epidemic model on homogeneous networks is considered. The largest Lyapunov exponent is calculated by Oseledec multiplicative ergodic theory, and the stability condition is determined by the largest Lyapunov exponent. The probability density function for the proportion of infected individuals is found explicitly, and the stochastic bifurcation is analysed by a probability density function. In particular, the new basic reproductive number R*, that governs whether an epidemic with few initial infections can become an endemic or not, is determined by noise intensity. In the homogeneous networks, despite of the basic productive number R0 > 1, the epidemic will die out as long as noise intensity satisfies a certain condition.
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