Abstract
A delayed computer virus spreading model in the network with limited anti-virus ability is proposed in the present paper. Local stability and the existence of a Hopf bifurcation are proved by taking the time delay as the bifurcation parameter and analyzing the distribution of the roots of the corresponding characteristic equation. Furthermore, properties of the Hopf bifurcation are investigated by using the normal form theory and the center manifold theorem. Finally, a numerical example is presented to demonstrate our obtained results.
Highlights
With the rapid development of computer technology and network communication technology, more and more functionalities and facilities have been brought to us by the network
It should be pointed out that system ( ) neglects the time delay due to the latent period of computer viruses in the exposed computers and the time delay due to the period that anti-virus software uses to clean the viruses in the infected computers
Γ E(t – R(t), τ where τ is the time delay due to the latent period of computer viruses in the exposed computers and τ is the time delay due to the period that anti-virus software uses to clean the viruses in the infected computers
Summary
With the rapid development of computer technology and network communication technology, more and more functionalities and facilities have been brought to us by the network. Xu and Ren [ ] proposed the following SEIR computer virus spreading model in the network with (t) + γ R(t), E(t) where S(t), E(t), I(t) and R(t) denote the numbers of the susceptible computers, the exposed computers where computer viruses are latent, the infected computers where computer viruses are breaking out and the recovered computers that have been equipped with anti-virus software at time t, respectively.
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