Abstract
ABSTRACTIn this paper, a computer virus propagation model with two delays and infectivity in latent period is investigated. First, the conditions which guarantee the local stability of the positive equilibrium and the existence of the Hopf bifurcation are derived by choosing the different combination of the two delays as the bifurcation parameter. Moreover, some specific properties for determining the stability and direction of the Hopf bifurcation are obtained by employing the normal form theory and the centre manifold theorem. Finally, a numerical simulation is carried out to verify the correctness of our obtained theoretical analysis.
Highlights
As the world becomes more electronically connected, computers connected to a network become more and more vulnerable to digital threats
The conditions which guarantee the local stability of the positive equilibrium and the existence of the Hopf bifurcation are derived by choosing the different combination of the two delays as the bifurcation parameter
A computer virus propagation model with two delays and infectivity in latent period was proposed by introducing the latent delay
Summary
As the world becomes more electronically connected, computers connected to a network become more and more vulnerable to digital threats. In the real network, on adequate contact with an infectious computer, a susceptible computer may become exposed, that is, infected but not yet infectious Based on this consideration, stability of the SEIR (susceptible-exposedinfectious-removed) computer virus model has been studied in Mishra and Pandey (2011), Peng, He, Huang, and Dong (2013) and Yuan and Chen (2008). Mishra and Pandey (2011), Peng et al (2013) and Yuan and Chen (2008) assumed that the recovered computers have a permanent immunization period and can no longer be infected This is not consistent with the reality in the real network. Zhang and Yang (2013) studied an SEIRS computer virus model with two delays and analysed Hopf bifurcation of the model They assume that the computers in latent period have no infectivity.
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