A SEIQR Model considering the Effects of Different Quarantined Rates on Worm Propagation in Mobile Internet

Abstract

At present, Wi-Fi is a common medium for connecting smart devices to networks in factories. The application of mobile Internet in smart manufacturing system (SMIS) speeds up the process of smart manufacturing but also increases SMIS vulnerability to worm attack from mobile networks. In this paper, we propose a new SLBQR (susceptible-latent-breaking out-quarantined-recovered) model considering vaccination strategies with temporary immunity and quarantined strategies. Based on basic reproduction number, we give expression of quarantined rate φ and obtain the threshold ϕ∗ of quarantined rate φ such that the worm-free equilibrium is asymptotically stable when ϕ≥ϕ∗, implying that the worm dies out eventually and its attack remains under control; the endemic equilibrium is asymptotically stable when φ<φ∗, namely, the worm is always persistent and spreading within a population. Hence, we give the quarantined strategy ϕ≥ϕ∗ to suppress the spread of virus. In addition, by theoretical analysis, we can conclude that even if the immunity time is unlimited, endemic equilibrium will not become worm-free. In other words, there is a mutation in the virus, which proves that there is no vaccination strategy with permanent immunity. Finally, we simulate our model with different temporary immune time and quarantine rates, and the results verify our theorem.