中国物理B ›› 2009, Vol. 18 ›› Issue (12): 5111-5116.doi: 10.1088/1674-1056/18/12/003

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A stochastic epidemic model on homogeneous networks

刘茂省1, 阮炯2   

  1. (1)Department of Mathematics, North University of China, Taiyuan 030051, China;School of Mathematical Sciences, Fudan University, Shanghai 200433, China; (2)School of Mathematical Sciences, Fudan University, Shanghai 200433, China
  • 收稿日期:2009-03-24 修回日期:2009-05-16 出版日期:2009-12-20 发布日期:2009-12-20
  • 基金资助:
    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).

A stochastic epidemic model on homogeneous networks

Liu Mao-Xing(刘茂省)a)b)† and Ruan Jiong(阮炯)b)   

  1. a Department of Mathematics, North University of China, Taiyuan 030051, China; b School of Mathematical Sciences, Fudan University, Shanghai 200433, China
  • Received:2009-03-24 Revised:2009-05-16 Online:2009-12-20 Published:2009-12-20
  • Supported by:
    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).

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摘要： 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.

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.

Key words: homogeneous networks, SIS epidemic model, stochastic stability, stochastic bifurcation

中图分类号:  (Networks and genealogical trees)

  • 89.75.Hc
02.30.Oz (Bifurcation theory) 02.50.Cw (Probability theory) 05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion) 87.10.-e (General theory and mathematical aspects)