SHIS Model of E-mail Virus Propagation

By analyzing the characteristics of many E-mail viruses in reality, we address an SHIS (Susceptiblehidden- infected-susceptible) model in this paper. In our model, on the one hand, the state H is introduced, which denotes user receives some E-mails with virus but s/he doesn’t activate them and they aren’t infectious. On the other hand, the topology of E-mail network is considered. The model not only describes better the practical condition of E-mail virus propagation than existing models, but also makes it possible to analyze the users’ behavior. By analyzing the rate equation of the model, we study the epidemic threshold and the equilibrium point. We also present the relationship between the infected density and two important parameters: the percentage of activating Email with virus and the frequency, in which users check the Email box. Finally, some numerical simulations are also presented to show the correctness of theoretical analysis. Our model would help to understand and control E-mail virus spreading.