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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.

##### MSC:
 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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