A computer virus model with graded cure rates.

*(English)* Zbl 1258.68020
Summary: 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, $R_{0}$, for this model is determined. Second, by introducing appropriate Lyapunov functions, it is proved that the virus-free equilibrium is globally asymptotically stable if $R_{0}\leq 1$, whereas the viral equilibrium is globally asymptotically stable if $1<R_{0}\leq 4$. Next, the sensitivity analysis of $R_{0}$ to three system parameters is conducted, and the dependence of $R_{0}$ on the remaining system parameters is investigated. On this basis, a set of policies is recommended for eradicating viruses spreading across the Internet effectively.

##### MSC:

68M99 | Computer system organization |

93C15 | Control systems governed by ODE |

34K60 | Qualitative investigation and simulation of models |