A SEIQRS Computer Virus Propagation Model and Impulse Control With Two Delays

Abstract

Computer viruses have caused great harm and nasty effects on people's lives. Therefore, analyzing and establishing the corresponding mathematical model can help explore and study the propagation law of computer viruses. On this basis, we apply the theory of computer virus propagation dynamics by combining computer viruses and the variability of their removal rates of different states in the network. The study presents a new Susceptible-Exposed-Infected-Quarantine-Recovered-Susceptible (SEIQRS) computer virus propagation model with two delays. In addition, we introduce impulse control, an optimal control method, to explore the effect of the impulse period on the model. We first derive the basic reproduction number of the model. Then, the characteristic equations and eigenvalues are discussed analytically by controlling the delay parameters variation in order to analyze local stability and Hopf bifurcation for the computer virus model. Next, we add impulse control and find that it could better control the propagation of computer viruses. Firstly, we analyze the dynamical behavior of this model using the relevant theories of time delay differential equations to provide a theoretical basis for the effective elimination and control of virus propagation in computer networks. Secondly, we use Matlab to conduct numerical simulations, which verify the correctness of theoretical results. Finally, we synthesize the theoretical and experimental analysis of the present model to provide some scientific suggestions for better control of the spreading of computer viruses.