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Stability analysis of a computer virus model in latent period. (English) Zbl 1352.68019

Summary: Based on a set of reasonable assumptions, the dynamical features of a novel computer virus model in latent period is proposed in this paper. Through qualitative analysis, we obtain the basic reproduction number \(R_0\). Furthermore, it is shown that the model have a infection-free equilibrium and a unique infection equilibrium (positive equilibrium). Using Lyapunov function theory, it is proved that the infection-free equilibrium is globally asymptotically stable if \(R_0<1\), implying that the virus would eventually die out. And by means of a classical geometric approach, the infection equilibrium is globally asymptotically stable if \(R_0>1\). Finally, the numerical simulations are carried out to illustrate the feasibility of the obtained results.

MSC:

68M10 Network design and communication in computer systems
34D05 Asymptotic properties of solutions to ordinary differential equations
37C75 Stability theory for smooth dynamical systems
92D30 Epidemiology
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