Computer Virus Propagation And Network Evolution Models

With the rapid popularization of the Internet and wireless networks, computerviruses are becoming increasingly rampant. Resisting electronic viruses with onlyantivirus software has turned out to be insufficient. It is regarded as an effectiveapproach to the resistance against viruses to understand the way viruses spread overnetworks and, thereby, to stipulate strategies for containing viruses. On the other hand,there is interaction between virus propagation and network evolution. Hence, it isnecessary to investigate how the virus propagation behavior affects the evolution of theunderlying network.The main contributions of this thesis are presented as follows.(1) To overcome some defects of the existing virus propagation models, a newvirus propagation model with stage immunization is proposed. The impact of thevarying probability of being vaccinated at the propagation threshold value on the spreadof the virus is examined. With the aid of the stability theory concerning dynamicalsystems, the existence and stability of the relevant equilibria are shown. Simulationresults show that both enhancing the vaccination rate and setting a reasonable thresholdvalue can effectively constrain the virus prevalence.(2) A non-growing network evolution model based on the susceptible-infective-susceptible (SIRS) propagation mechanism is proposed. Simulation results show that1)a higher average node degree is conducive to the infection of viruses; and2) the degreesequence of the resulting network follows a Poisson distribution approximately and,with the increasing average node degree and infection rate, the clustering coefficientand average inter-node distance of the resulting network shall rise up and fall down,respectively, showing the characteristics of small-world networks.The obtained results can help us to better understand the laws governing the spreadof computer viruses and the evolution of networks.