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Abstract and Applied Analysis
Volume 2014, Article ID 735327, 7 pages
http://dx.doi.org/10.1155/2014/735327
Research Article

Global Stability of a Computer Virus Propagation Model with Two Kinds of Generic Nonlinear Probabilities

1School of Software Engineering, Chongqing University, Chongqing 400044, China
2College of Computer Science, Chongqing University, Chongqing 400044, China

Received 1 April 2014; Accepted 4 June 2014; Published 26 June 2014

Academic Editor: Tonghua Zhang

Copyright © 2014 Chenquan Gan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Vaccination is one of the most effective measures for suppressing the spread of computer virus, and the bilinear incidence rate assumption for the majority of previous models, which is a good first approximation of the general incidence rate, is in disagreement with the reality. In this paper, a new dynamical model with two kinds of generic nonlinear probabilities (incidence rate and vaccination probability) is established. An exhaustive mathematical analysis of this model shows that (a) there are two equilibria, virus-free equilibrium and viral equilibrium, and (b) the virus-free (or viral) equilibrium is globally asymptotically stable when the basic reproduction number is less (or greater) than unity. The analysis of the basic reproduction number is also included. Additionally, some numerical examples are given to illustrate the main results, from which it can be seen that the generic nonlinear vaccination is helpful to strengthen computer security.