Three Novel Computer Virus Propagation Models

With the rapid popularization of computer networks, computer viruses arebecoming more and more rampant, yielding huge negative influence on human workand life. As a result, how to effectively contain the spread of viruses over networks hasbecome an important issue in the area of computer security.This thesis aims to study the laws governing virus propagation and the means ofcontaining virus spread. For that purpose, three novel computer virus propagationmodels are proposed and, on this basis, some effective measures to prohibit viruses aresuggested. Furthermore, a new network evolution mechanism is advised, and thecorresponding computer simulations validate the rationality of the proposed models.The main contributions of this thesis are presented below.①Under the assumption that the total number of computers in the world isapproaching a saturate value, a new propagation model, which is known as the SIESmodel, is proposed. The conditions for the stability of the two relevant equilibria aregiven, respectively. On this basis, some measures to control virus spread are suggested.②Under the more reasonable assumption that the total number of computers inthe world is changing, a modified SIES model is presented. Again, the conditions for thestability of the two relevant equilibria are given, respectively, and some measures tocontrol virus spread are suggested.③Taking into account the maintenance cost of computers, a controlled SIESmodel is proposed by introducing control variables into the modified SIES model. Thetotal index for the model is optimized employing the Pontryagin’s Minimum Principle.Simulation experiments justify the corresponding control strategy.④An SIES model based network evolution mechanism is proposed, and it isfound that the resulting networks possess small-world properties. To a certain extent,this result supports our SIES models.The obtained results benefit our understanding of the spread of computer virusesover networks and stipulation of policies for virus containment.