A stochastic epidemic model on homogeneous networks
Liu Mao-Xing(刘茂省)a)b)† and Ruan Jiong(阮炯)b)
a Department of Mathematics, North University of China, Taiyuan 030051, China; b School of Mathematical Sciences, Fudan University, Shanghai 200433, China
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 $R_0>1$, the epidemic will die out as long as noise intensity satisfies a certain condition.
Received: 24 March 2009
Revised: 16 May 2009
Accepted manuscript online:
Fund: Project supported by the Science
Foundation of Shanxi Province of China (Grant No 2009011005-1), the
Youth Foundation of Shanxi Province of China (Grant No 2007021006).
Cite this article:
Liu Mao-Xing(刘茂省) and Ruan Jiong(阮炯) A stochastic epidemic model on homogeneous networks 2009 Chin. Phys. B 18 5111
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