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A delayed computer virus propagation model and its dynamics. (English) Zbl 1343.34186
Summary: We propose a delayed computer virus propagation model and study its dynamic behaviors. First, we give the threshold value \(R_0\) determining whether the virus dies out completely. Second, we study the local asymptotic stability of the equilibria of this model and it is found that, depending on the time delays, a Hopf bifurcation may occur in the model. Next, we prove that, if \(R_0=1\), the virus-free equilibrium is globally attractive; and when \(R_0 <1\), it is globally asymptotically stable. Finally, a sufficient criterion for the global stability of the virus equilibrium is obtained.

MSC:
34K60 Qualitative investigation and simulation of models involving functional-differential equations
92D30 Epidemiology
34K20 Stability theory of functional-differential equations
34K18 Bifurcation theory of functional-differential equations
34K13 Periodic solutions to functional-differential equations
34K25 Asymptotic theory of functional-differential equations
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