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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 161509, 9 pages
http://dx.doi.org/10.1155/2014/161509
Research Article

Global Dynamics of Infectious Disease with Arbitrary Distributed Infectious Period on Complex Networks

1School of Mechatronic Engineering, North University of China, Taiyuan, Shanxi 030051, China
2Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China
3Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, China

Received 6 July 2014; Accepted 19 August 2014; Published 1 September 2014

Academic Editor: Sanling Yuan

Copyright © 2014 Xiaoguang Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Most of the current epidemic models assume that the infectious period follows an exponential distribution. However, due to individual heterogeneity and epidemic diversity, these models fail to describe the distribution of infectious periods precisely. We establish a SIS epidemic model with multistaged progression of infectious periods on complex networks, which can be used to characterize arbitrary distributions of infectious periods of the individuals. By using mathematical analysis, the basic reproduction number for the model is derived. We verify that the depends on the average distributions of infection periods for different types of infective individuals, which extend the general theory obtained from the single infectious period epidemic models. It is proved that if , then the disease-free equilibrium is globally asymptotically stable; otherwise the unique endemic equilibrium exists such that it is globally asymptotically attractive. Finally numerical simulations hold for the validity of our theoretical results is given.