Research Article Global Dynamics of Infectious Disease with Arbitrary Distributed Infectious Period on Complex Networks Xiaoguang Zhang, 1,2 Rui Song, 2 Gui-Quan Sun, 2,3 and Zhen Jin 2,3 1 School of Mechatronic Engineering, North University of China, Taiyuan, Shanxi 030051, China 2 Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China 3 Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, China Correspondence should be addressed to Zhen Jin; jinzhn@263.net Received 6 July 2014; Accepted 19 August 2014; Published 1 September 2014 Academic Editor: Sanling Yuan Copyright © 2014 Xiaoguang Zhang et al. Tis 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. 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  0 for the model is derived. We verify that the  0 depends on the average distributions of infection periods for diferent types of infective individuals, which extend the general theory obtained from the single infectious period epidemic models. It is proved that if  0 <1, 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. 1. Introduction Te infectious period of an infective individual means the period during which an infected person has a probability of transmitting the virus to any susceptible host or vector they contact. Note that the infectious period may be associated with the ftness of persons. Te infuence degrees of infection and rates of disease transmission are varied for individuals with diferent infectious periods. Every year, some emerging infectious diseases with unknown infectious period are seri- ously threatening the health of people. Tere is no doubt that the defciency of the infectious period’s knowledge results in the difculty of controlling epidemic. Ten, in order to obtain the date of the infectious period of these epidemics in medicine, a large amount of statistics data is necessary. However, it is hard to get the date in the early stage of the disease. Terefore applying mathematical methods to research the efects of infectious period distribution on the infectious diseases spread is signifcative. As the SIS compartment model was frst proposed by Kermack and McKendrick in 1932 [1], thousands of scien- tists successively started to study the epidemic propagation by mathematic models [2–4]. In most of their models, infected compartment contains all infected individuals and the proportion of infected individuals who transit into the next state per unit time is a constant . Wearing et al. [5] pointed out that the assumption of exponentially distributed infectious periods always results in underestimating the basic reproductive ratio of an infection from outbreak data. According to the staged progression features of HIV or TB, Lloyd [6] applied gamma distribution to describe the infectious period distribution. However, the distributions of the infectious period of a lot of infectious diseases in the real world may not satisfy exponent or gamma distribution. Ten, Feng et al. [7] used integral-diferential equations to study the nonexponential distribution of the infectious period. Te homogeneous mixing models, they considered, ignore the heterogeneity of contacts of individuals. Hindawi Publishing Corporation Discrete Dynamics in Nature and Society Volume 2014, Article ID 161509, 9 pages http://dx.doi.org/10.1155/2014/161509