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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 1, whereas the viral equilibrium is globally asymptotically stable if 1<R 0 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:
68M99Computer system organization
93C15Control systems governed by ODE
34K60Qualitative investigation and simulation of models