A stochastic epidemic model on homogeneous networks |
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Authors: | Liu Mao-Xing and Ruan Jiong |
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Affiliation: | Department of Mathematics, North University of China, Taiyuan 030051, China; School of Mathematical Sciences, Fudan University, Shanghai 200433, China |
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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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Keywords: | homogeneous networks SIS epidemic model stochastic
stability stochastic bifurcation |
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