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

Author

Listed:
  • Chenquan Gan
  • Xiaofan Yang
  • Qingyi Zhu

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.

Suggested Citation

  • Chenquan Gan & Xiaofan Yang & Qingyi Zhu, 2014. "Global Stability of a Computer Virus Propagation Model with Two Kinds of Generic Nonlinear Probabilities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:735327
    DOI: 10.1155/2014/735327
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    References listed on IDEAS

    as
    1. Tao Dong & Xiaofeng Liao & Huaqing Li, 2012. "Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, April.
    2. Tao Dong & Xiaofeng Liao & Huaqing Li, 2012. "Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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