Effects of computer networks' viruses under the of removable devices

Abstract

The removable devices (RD) is one of the important factors that affects the virus spreading. We assumed that the infected RD could affect the nodes of S and E compartments at the rates, θ1 and θ2, respectively. While the previous studies considered this effect on susceptible compartment only. Moreover, we considered the effect of the rate of the nodes which are break down from network because of infected RD, μ1. This model has no virus-free equilibrium and has a unique endemic equilibrium. The theorems of asymptotically autonomous systems and the generalised Poincare-Bendixson are used to show that the endemic equilibrium is globally asymptotically stable. Numerical methods are used to solve the obtained system of differential equations and the solutions are illustrated in several examples. The effects of ξ, ϵ, θ1 and θ2 rates on the devices that moved from latent to recovered nodes are investigated.