Dynamics of Epidemic Computer Virus Spreading Model with Delays

Abstract

The vulnerability that exists in the computer network by the infection of virus as soon as the resources are exposed requires the study of the nature of propagation of virus into the network. In this work we have formulated a novel epidemic Susceptible-Infected-Recovered model that deals with the infected nodes in the network in terms of the development of immunity attained after recovery. Positivity and boundedness of the proposed model is examined. Local stability analysis of the proposed model without delay is also analyzed by Routh–Hurwitz criteria apart from the delay sensitivity analysis. The time series analysis regarding the nature of the susceptible, infected and recovered nodes in the network has been performed using real control parameters $$\beta$$ (infection rate of the computers), $$\gamma$$ (recovered rate of the infected computers). We also analyzed that time delay may play significant role on the stability of the proposed model since whenever delay exceeds the critical value the system loses its stability and a Hopf bifurcation occurs. The numerical simulation results justify that the proposed model is validated against the analytical studies of virus propagation thus verifying the theoretical results.