%0 Journal Article
%T A New Model for Capturing the Spread of Computer Viruses on Complex-Networks
%A Chunming Zhang
%A Tianliang Feng
%A Yun Zhao
%A Guifeng Jiang
%J Discrete Dynamics in Nature and Society
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/956893
%X Based on complex network, this paper proposes a novel computer virus propagation model which is motivated by the traditional SEIRQ model. A systematic analysis of this new model shows that the virus-free equilibrium is globally asymptotically stable when its basic reproduction is less than one, and the viral equilibrium is globally attractive when the basic reproduction is greater than one. Some numerical simulations are finally given to illustrate the main results, implying that these results are applicable to depict the dynamics of virus propagation. 1. Introduction Computer viruses, including the narrowly defined viruses and network worms, are loosely defined as malicious codes that can replicate themselves and spread among computers. Usually, computer viruses attack computer systems directly, while worms mainly attack computers by searching for system or software vulnerabilities. With the rapid popularization of the Internet and mobile wireless networks, network viruses have posed a major threat to our work and life. To thwart the fast spread of computer viruses, it is critical to have a comprehensive understanding of the way that computer viruses propagate. Kephart and White [1] proposed the first epidemiological model of computer viruses. From then on, much effort has been done in developing virus spreading models [1¨C15]. On the other hand, it was found [16¨C18] that the Internet topology follows the Ħ°scale-freeĦħ (SF) networks; that is, the probability that a given node is connected to other nodes follows a power-law of the form , with the remarkable feature that for most real-world networks. This finding has greatly stimulated the interest in understanding the impact of network topology on virus spreading [16¨C29]. Recently, Mishra and Jha [2] investigated a so-called SEIQRS model on a homogeneous network by making the following assumptions.(H1)The population has a homogeneous degree distribution.(H2)The total population of computers is divided into five groups: susceptible, exposed, infected, quarantine and recovered computers. Let , , , , and denote the numbers of susceptible, exposed, infected, quarantine, and recovered computers, respectively.(H3)New computers are attached to the Internet at rate .(H4)Computers are disconnected from the Internet naturally at a constant rate and removed with probability due to the attack of malicious objects.(H5) computers become with constant rate ; computers become with constant rate ; computers become with constant rate ; computers become with constant rate ; computers become with constant rate ; computers
%U http://www.hindawi.com/journals/ddns/2013/956893/