Lyapunov Approach in Global Asymptotic Stability of an Epidemic Model of Computer Viruses

Abstract

The aim of this work is to study a system of first order ordinary differential equations is used to analyse the dynamics of computer viruses via a mathematical model proposed. The global stability analysis is conducted for the extended model by suitable Lyapunov function, interesting only on internal computers connected to the internet which they are classified to uninfected computers (i.e., virus-free computers), infected computers that are currently latent and infected computers that are currently breaking. The basic reproduction number R0 can be played role in determining whether the virus will extinct or persist, if R0 < 1 then the virus-free equilibrium is globally asymptotically stable and unstable when R0> 1 . Hence, we suggest some aspects for future research, which are : when R0= 1 . Are the disease-free and endemic equilibrium asymptotically stable?