Modeling And Impulsive Control Of Computer Viruses Propagation

As we know, computers and communication networks have been an indispensablepart of our learning, work and life. Having suffered from many unprecedented attacks ofelectronic viruses, it has become an urgent task in the field of information security tokeep computers away from viruses. As powerful means of fighting against viruses,antivirus software, security guard and firewall are installed in nearly all computers. Dueto a variety of reasons, however, the development of antivirus software is deemed tolags behind that of virus. As a result, antivirus technique seems to be ineffective whenconfronted with new types of viruses. The propagating dynamics of computer viruses,which emerged in1991, is devoted to understand the way that computer viruses spreadover networks and, thereby, work out effective policies to contain their prevalence.Inspired by previous work in this area and based on our insight into thevirus-spreading mechanism, this thesis proposes and studies three novel propagatingmodels of computer viruses. Specifically, the main contributions made in this thesis arepresented below.1. Considering the influence of countermeasure competing strategy (CMC) on thepropagation of viruses, a new virus propagation model, which is known as the SICSmodel, is proposed. Theoretical study shows that this model admits at most twovirus-free equilibria and two viral equilibria. The global stabilities of these fourequilibria are fully investigated, respectively, accompanied with numerical examples.2. What predators mean are benevolent, self-propagating programs that have theability to clean up systems infected by malignant worms/viruses. Under this context, amodel describing the coevolution of viruses and predators, which is known as the SIPSmodel, is proposed. Theoretical inspection demonstrates that, to the maximum, thismodel has one virus-free equilibrium and two viral equilibria. The global stabilities ofthese three equilibria are fully examined. Numerical examples support our results.3. By incorporating the influence of removable devices in the classical SIR model,a new epidemic model of computer viruses is advised. Theoretical investigation informsthat the model has one virus-free equilibrium and at most one viral equilibrium. Theconditions for the global stability of these two equilibria are given, respectively.Numerical examples are in good agreement with the theoretical conclusions.4. By imposing an impulsive control strategy on an SIR delayed model, a new epidemic model with pulse is proposed. Theoretical analysis shows that (1) the modelhas a virus-free periodic solution,(2) the periodic solution is globally attractive underproper conditions, and (3) the system is uniformly persistent under moderate conditions.A few numerical examples are also given.