Bifurcation analysis of an e-SEIARS model with multiple delays for point-to-group worm propagation

Zizhen Zhang,Tao Zhao

doi:10.1186/s13662-019-2164-7

Abstract

In this paper, by taking two important network environment factors (namely point-to-group worm propagation and benign worms) into consideration, a mathematical model with multiple delays to model the worm prevalence is presented. Sufficient conditions for the local stability of the unique endemic equilibrium and the existence of a Hopf bifurcation are demonstrated by choosing the different combinations of the three delays and analyzing the associated characteristic equation. Directly afterward, the stability and direction of the bifurcated periodic solutions are investigated by using center manifold theorem and the normal form theory. Finally, special attention is paid to some numerical simulations in order to verify the obtained theoretical results.

Highlights

Over the years coupled with the fast development of communication technology and computer network applications, the network security has become an important challenge to the internet [1]
Computer worms are selfreplicating programs created to carry out activities, which can quickly infect millions of electronic devices without consent of their owners, and they have brought about huge economic losses and have had high social impact [2, 3]
Based on a newfangled observation that the spread of worms among computers is closely similar to the transmission of the infectious disease among a population, many epidemic models, such as SIRS model [4], SEIR model [5], SEIRS [2, 6, 7] model, SEIS-V model [8], SEIQR model [9] and SEIRS-V model [10,11,12], have been employed to analyze and describe the spread of computer worms in the internet

Summary

Introduction

Over the years coupled with the fast development of communication technology and computer network applications, the network security has become an important challenge to the internet [1]. Based on a newfangled observation that the spread of worms among computers is closely similar to the transmission of the infectious disease among a population, many epidemic models, such as SIRS model [4], SEIR model [5], SEIRS [2, 6, 7] model, SEIS-V model [8], SEIQR model [9] and SEIRS-V model [10,11,12], have been employed to analyze and describe the spread of computer worms in the internet. As stated in the literature [13], the “point-to-group” (P2G), is extensively exists in the real world, especially in information sharing network. Its typical characteristics is that the group members in such network environment can receive the message or file

Zhang and Zhao Advances in Difference Equations

Conclusions