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| In this paper, a dynamical model characterizing the spread of computer viruses over the Internet is established, in which two assumptions are imposed: (1) the anti-virus strategy is discontinuous and (2) a computer possesses infectivity once it is infected. The qualitative properties of this model are fully studied. First, the basic reproduction number is determined, which describes the structure of possible equilibria as well as establishes the stability/instability of the equilibria. Second, we find that in the case that the virus-free equilibrium is asymptotically stable, the convergence to the virus-free equilibrium can actually be achieved in finite time, and we can estimate this time in terms of the model parameters, the initial number of the latent computer and breaking out computer and the initial anti-virus strength. This suggests that from the view point of eliminating the virus from the Internet, discontinuous anti-virus strategies would be superior to continuous ones. Finally, an illustrative example is also given to support the theoretical results. |
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| Keywords:Global Stability, Discontinuous, Computer virus, Dynamical model, Finite time |
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