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A stochastic SIR epidemic on scale-free network with community structure

Authors:	Huiling Zhang Zhi-Hong Guan Tao Li Xian-He Zhang Ding-Xue Zhang

Affiliation:	1. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, PR China;2. Electronics and Information College, Yangtze University, Jingzhou, 434023, PR China;3. College of Mechatronics and Control Engineering, Hubei Normal University, Huangshi, 435002, PR China;4. Petroleum Engineering College, Yangtze University, Jingzhou, 420400, PR China

Abstract:	The scale-free degree distribution and community structure are two significant properties shared by numerous complex networks. In this paper, we investigate the impact of these properties on a stochastic SIR epidemic which incorporates the stochastic nature of epidemic spreading. A two-type branching process is employed to approximate the early stage of epidemic spreading. The basic reproduction number _R₀ $R_{0}$ is obtained. And the influences of scale-free property and community structure on _R₀ $R_{0}$ are analyzed by numerical simulations.

Keywords:	Scale-free network Community structure Stochastic epidemic Basic reproduction number
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