A computer virus model with graded cure rates

Abstract

A dynamical model characterizing the spread of computer viruses over the Internet is established, in which two assumptions are imposed: (1) a computer possesses infectivity once it is infected, and (2) latent computers have a lower cure rate than seizing computers. The qualitative properties of this model are fully studied. First, the basic reproduction number, R0, for this model is determined. Second, by introducing appropriate Lyapunov functions, it is proved that the virus-free equilibrium is globally asymptotically stable if R0≤1, whereas the viral equilibrium is globally asymptotically stable if 1<R0≤4. Next, the sensitivity analysis of R0 to three system parameters is conducted, and the dependence of R0 on the remaining system parameters is investigated. On this basis, a set of policies is recommended for eradicating viruses spreading across the Internet effectively.