Dynamics of virus-patch model with latent effect

Abstract

A deterministic nonlinear mathematical model that describes the virus and patch propagation with latency in infection has been developed and the effect of patching is explored. The basic reproduction number $R_0$ of the virus-patch dynamics is computed. The virus-patch model exhibits two virus-free and two endemic states with and without patched nodes. The virus can be removed from the network by enhancing the patching rate $(\beta )$ and curability rate $({\gamma }_2)$ of latent nodes. The local stability conditions of all the four equilibrium states are obtained. Further, the computer virus may be eliminated from the network for $R_0>1$ by enhancing the patching rate or reducing the patch invalidation rate (${\gamma }_1$). A bifurcation diagram with respect to patching rate $(\beta )$ and basic reproduction number $(R_0)$ is obtained. The diagram bifurcates the parameter space into regions of stable disease free and endemic states of the model.

Keywords:

• Computer virus
• Basic reproduction number
• Dynamical system
• Stability
• Bifurcation

2020 AMS Subject Classification:

• 37C75

Acknowledgments

The first author is thankful to All India Council for Technical Education (AICTE), Government of India for funding this research.

Disclosure statement

No potential conflict of interest was reported by the author(s).