The Impact of the Network Topology on the Viral Prevalence: A Node-Based Approach.

Lu-Xing Yang,Moez Draief,Xiaofan Yang,Gui-Quan Sun

doi:10.1371/journal.pone.0134507

Lu-Xing Yang, Moez Draief + Show 2 more

Open Access

https://doi.org/10.1371/journal.pone.0134507

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Journal: PloS one	Publication Date: Jul 29, 2015
Citations: 98	License type: CC BY 4.0

Affiliation: Imperial College London, Chongqing University

Abstract

This paper addresses the impact of the structure of the viral propagation network on the viral prevalence. For that purpose, a new epidemic model of computer virus, known as the node-based SLBS model, is proposed. Our analysis shows that the maximum eigenvalue of the underlying network is a key factor determining the viral prevalence. Specifically, the value range of the maximum eigenvalue is partitioned into three subintervals: viruses tend to extinction very quickly or approach extinction or persist depending on into which subinterval the maximum eigenvalue of the propagation network falls. Consequently, computer virus can be contained by adjusting the propagation network so that its maximum eigenvalue falls into the desired subinterval.

Highlights

The rapidly popularized Internet has brought us lots of benefits
To understand the way that the spread of virus on a network is affected by the structure of the network, a new epidemic model of computer virus has been proposed
The model analysis reveals that the maximum eigenvalue of the network is a key factor determining the viral prevalence; viruses tend to extinction very quickly or approach extinction or persist depending on where the maximum eigenvalue of the network lies

Summary

Introduction

The rapidly popularized Internet has brought us lots of benefits. On the flip side of the coin, computer viruses can propagate their replicates through the Internet much more rapidly than ever before, resulting in great disruptions. Since Kephart and White’s seminal work on the compartment modeling of computer viruses in the early 1990s [1, 2], a multitude of compartment-based computer virus propagation models, ranging from the SIR models [3] and the SIRS models [4, 5] to the SEIRS models [6], have been suggested. Most of these models are suited to infectious diseases and computer viruses well.

Preliminaries

A brief review of the compartment-based SLBS models

The new computer virus epidemic model

Model analysis

Numerical examples

Further discussions

Conclusions and remarks