HOPF- bifurcation analysis of delayed computer virus model with holling type iii incidence function and treatment

Abstract

Computer viruses have become a threatening challenge to most network users. Due to enormous operational constraints, distortions, and alterations caused by malware spread, research on network security is deemed essential. These malicious codes are sufficiently equipped to distribute themselves over the whole system. Consequently, infected hosts can rapidly pollute adjoining nodes. In the past, many research efforts have derived analytical models for computer viruses under several scenarios of infectiousness. Therefore, we considered the Susceptible-Exposed-Infectious-Recovered-Vaccinated (SVEIR) model with Holling Type III incidence function and treatment. This is to address the ubiquitous application of the bilinear contagion rate. Here, the delay parameter was chosen and, through numerous analyses, we demonstrated the presence of a Hopf bifurcation as it crosses a critical value. Furthermore, we examined the attributes of the Hopf bifurcation by employing the centre manifold theorem and the normal form theory. Then, we performed numerical simulation experiments for different conditions in order to underpin the derived theoretical conclusions.

Keywords

• Computer virus model
• Hopf-Bifurcation
• Delayed model