Three Novel Computer Virus Propagation Models: Theoretical Study And Application Strategies

Since its birth in the early1980s, computer virus (virus, for short) has lead to greateconomic loss and social scare. With the popularity of network as means of sharinginformation and, especially, with the advent of era of the Internet of Things, the waythat virus spreads exhibits multi-type, hidden, speeding and intelligent properties, whichsignificantly enhances the threat to information society. Consequently, it is an importanttask to decrease the danger of computer virus based on multi-level andmulti-dimensional study.There are two basic categories of research methods of computer virus: themicroscopic method and the macroscopic method. As the most popular method forfighting against virus, the micro-level study aims, by studying the logic structure orbehavior of virus, to develop programs that can detect and clear virus effectively. Themicroscopic method, however, suffers from the disadvantage that it cannot provide afar-reaching insight into the future trend of computer virus. The macroscopic study ofcomputer virus, which has received considerable interest in the past decade or so, isintended to establish dynamical models that can reflect the propagation feature of virus,to understand the laws governing its propagation through the analysis of models, and topropose measures by which the spread of virus can be controlled. The macroscopicmethod for the study of virus is supplementary to its microscopic study.This thesis aims, by fully considering the features of propagation of virus, tointroduce new models characterizing the spread of virus, to obtain profound resultsconcerning these models through thorough theoretical study as well as numericalsimulations, and to apply the results obtained to the control of virus. The maincontributions achieved in this thesis are presented below.First, considering the fact that a latent networked node (computer) possesses passiveinfectivity, a new virus propagation model, which is known as the SLBRS model, isproposed. The results concerning this model include the following:(1) Two equilibria,the virus-free equilibriumE0and the viral equilibriumE*, as well as the basicreproduction ratioR0are found.(2) The dynamical behavior is determined completelyby the value ofR0:R01implies the global stability ofE0, whereasR01implies the global stability ofE*.(3) By conducting a sensitive analysis ofR0withrespect to various model parameters and on the condition thatR01, a series of measures of strategies is proposed for controlling the spread of virus through theInternet effectively.Second, considering the fact that a node that is performing the behaving model of avirus has a higher cure rate than a latent node, and by modifying the previous SLBRSmodel, a virus propagation model with graded cure rates is proposed. The resultsconcerning this model include the following:(1) The virus-free equilibriumE0and theviral equilibriumE*, as well as the basic reproduction ratioR0are found.(2) It isproved thatR01implies the global stability ofE0, and thatR01implies theglobal stability ofE*.(3) By conducting a sensitive analysis ofR0with respect tovarious model parameters and on the condition thatR01, a collection of policies isrecommended for controlling viruses spreading across the Internet effectively.Third, considering the feature of resident virus and the fact that the passive infectionrate of a latent node is lower than the active infection rate of a behaving node, a newresident virus propagation model with graded infection rates, which is known as theSLARS model, is proposed. The results concerning this model include the following:(1)Two equilibria, the virus-free equilibriumE0and the viral equilibriumE*, as well asthe basic reproduction ratioR0are found.(2) The dynamical behavior is determinedcompletely by the value ofR0:R01implies the global stability ofE0, whereasR01implies the global stability ofE*.(3) By conducting a sensitive analysis ofR0with respect to various model parameters and on the condition thatR01, a setof measures of strategies is proposed for controlling the spread of resident virus throughthe Internet effectively.Finally, the work done in this thesis is summarized, and some future research topicsare indicated.