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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 \(R_{0}\leq 1\), 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.

68M99 Computer system organization
93C15 Control/observation systems governed by ordinary differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
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