Dynamical Analysis of a Computer Virus Propagation Model with Delay and Infectivity in Latent Period

Zizhen Zhang,Dianjie Bi

doi:10.1155/2016/3067872

Abstract

A delayed SLB computer virus propagation model with infectivity in latent period is proposed in this paper. We establish sufficient conditions for local stability of the positive equilibrium and existence of Hopf bifurcation by analyzing distribution of the roots of the associated characteristic equation and applying the Hopf bifurcation theorem. Furthermore, properties of the Hopf bifurcation are determined by using the normal form theory and the center manifold theorem. Finally, numerical simulations supporting the theoretical analysis are carried out.

Highlights

Due to their striking features such as destruction, polymorphism, and unpredictability [1,2,3], computer viruses, ranging from conventional viruses to network worms and other malicious codes such as Trojans and spyware, have addressed a serious threat to confidentiality, integrity, and availability of computer resources on the Internet
A new epidemic model of computer virus with time delay has been proposed in this paper
Compared with the model considered in the literature [8], we mainly investigate the effect of the delay due to the period that a computer user uses to cure the latent and breaking-out computers by using antivirus software or reinstalling system on system (2) by analyzing the corresponding characteristic equation and regarding the time delay as a bifurcation parameter

Summary

Introduction

Due to their striking features such as destruction, polymorphism, and unpredictability [1,2,3], computer viruses, ranging from conventional viruses to network worms and other malicious codes such as Trojans and spyware, have addressed a serious threat to confidentiality, integrity, and availability of computer resources on the Internet. Because computer viruses have a feature of latency, an infected computer which is in latency can infect other computers through file copying or file downloading Based on this consideration, in [8], Yang et al proposed the following computer virus model with graded cure rate: dS (t) dt. System (1) ignores time delay due to the period that a computer user uses to cure the latent and the breakingout computers by using antivirus software or reinstalling system. Motivated by the work above, we introduce the time delay due to the period that a computer user uses to cure the latent and breaking-out computers into system (1) and get the following delayed computer virus model: βS (t) (L (t).

Existence of Hopf Bifurcation

Properties of the Hopf Bifurcation

Numerical Simulation

Conclusion