Modeling, Analysis And Control Of The Spread Of Computer Virus

The past few decades have witnessed a rapid popularization of the Internet and wireless networks. This popularization, however, also greatly enhances the propagation capability of computer viruses. Due to their striking features such as destruction, polymorphism, and unpredictability, computer viruses have come to be one major threat to the contemporary information society. With the rapid progress of computer and communication technologies, computer virus programs are becoming increasingly sophisticated so that developing antivirus software is becoming increasingly time-consuming and expensive. Most unfortunately, traditional measures of defending against computer viruses, ranging from firewall to antivirus software, are incompetent to inhibit virus diffusion over the Internet. Dynamical modeling of the spread process of computer viruses is an effective approach to understanding the behavior of computer viruses because, on this basis, some effective measures can be posed to prevent infection.The aims of this thesis are to establish rational dynamical models underlying the mechanism of the spread of computer virus, analyze the global dynamics of the proposed models theoretically and experimentally, and work out some effective measures for controlling viral spread. The major contributions made in this thesis are as follows.â‘  Two classes of SIRS(susceptible-infected-recovered-susceptible) models with linear vaccination probability and incidence rate are studied. Firstly, the dynamical behavior of an SIRS model with linear vaccination probability and linear incidence rate is examined. On this basis, this model is extended by considering generalized nonlinear vaccination probability and generalized nonlinear incidence rate. The global stabilities of two equilibria of the model are also proved.â‘¡ An SIRS model under the effects of infected external computers and infected removable storage media is considered. The global stability of the unique equilibrium of the model is shown theoretically and experimentally. A result for suppressing virus diffusion is conducted.â‘¢ An SLBRS(susceptible-latent-breaking-recovered-susceptible) model under the impacts of infected external computers and antivirus software is proposed and analyzed. The unique equilibrium of the model is globally asymptotically stable. Some numerical simulations are also made to show this result and the influences of external computers and antivirus software on viral spread.â‘£ Two classes of SIES(susceptible-infected-external-susceptible) models with external compartments are investigated. Firstly, a homogeneous SIES model is established. A qualitative analysis of this model shows that the unique equilibrium is globally asymptotically stable and the number of infected computers can be made below an acceptable threshold by taking effective measures. Based on this model, a heterogeneous SIES model, which incorporates the effect of the network topology on the spread of computer virus, is presented. The global attractivity of the unique equilibrium of the model is performed and illustrated. Furthermore, it is found that higher-degree nodes are more susceptible to infections than lower-degree nodes. In this regard, some appropriate protective measures are recommended.