Abstract
A delayed SEIRS-V model on the transmission of worms in a wireless sensor network is considered. Choosing delay as a bifurcation parameter, the existence of the Hopf bifurcation of the model is investigated. Furthermore, we use the normal form method and the center manifold theorem to determine the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions. Finally, some numerical simulations are presented to verify the theoretical results.
Highlights
In past several decades, many authors have studied different mathematical models which illustrate the dynamical behavior of the transmission of computer viruses based on the classical epidemic models due to the lots of similarities between biological viruses and computer viruses [ – ]
The main results are given in terms of local stability and local Hopf bifurcation
We have proven that when the conditions are satisfied, there exists a critical value τ of the delay below which system ( ) is stable and above which system ( ) is unstable
Summary
Many authors have studied different mathematical models which illustrate the dynamical behavior of the transmission of computer viruses based on the classical epidemic models due to the lots of similarities between biological viruses and computer viruses [ – ]. In order to study the attacking behavior of possible worms in a wireless sensor network and considering that there is a basic similarity between the software viruses spread among wireless devices and the transmission of epidemic diseases in a population, Mishra and Keshri [ ] proposed the following SEIRS-V model: Get the following delayed SEIRS-V system on the transmission of worms in a wireless sensor network:
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