Abstract
The mobile networks have increasingly facilitated our daily life but are also breeding grounds for malicious worms, which are considered as the main threat to cyber security. The purpose of this paper is to analyze the dynamics of worm propagation and to control the worm epidemic based on mobile-phone networks. Accordingly, we establish an SEIQR-type model to explore the worm epidemic with saturated incidence rate. This paper shows that if the basic reproduction number is less than 1, the worm-free equilibrium is asymptotically stable, and the epidemic of worm will eventually disappear and remain under control; in addition, if the basic reproduction number is greater than 1, the asymptotical stability of worm-existence equilibrium is derived to imply that the epidemic will remain persistent and uncontrollable. Our results give new insights to mobile network security, namely, that is predicting the worm spreading tendency, identifying the epidemic control strategies, and estimating the worm popularity level. Numerical experiments are conducted to show the rationality of our obtained results and the effectiveness of the control strategies.
Highlights
As everyone knows, the mobile devices, e.g., smartphones, tablets, and laptops, are increasingly pervasive in the world today but have been both the target and victim of network worm attackers
Compared with the previous papers, the novel ideas of our paper are that (a) the SEIQR model is along with the saturated rate of incidence; (b) the recovery process from the susceptible group to the recovered group is considered thanks to some sufficient defense mechanisms or antivirus treatments; (c) the dysfunction of devices relates to natural death and depends on worm-related death, because in the real world, the crash of most devices results from the attack of malicious worms; and (d) the worm epidemic intervention strategies are established by reducing its size and speed
We consider the general SEIQR-type worm propagation model, in which the mobile devices are divided into five groups: susceptible group (S) includes the devices uninfected by malicious worms but vulnerable to worm attacks; exposed group (E) includes the devices exposed to and infected by the worms but not infectious; infectious group (I) includes the exposed and infectious devices; quarantine group (Q) includes the infectious and quarantined devices; recovered group (R) includes the recovered devices with immunity against the worms
Summary
The mobile devices, e.g., smartphones, tablets, and laptops, are increasingly pervasive in the world today but have been both the target and victim of network worm attackers. Compared with the previous papers, the novel ideas of our paper are that (a) the SEIQR model is along with the saturated rate of incidence; (b) the recovery process from the susceptible group to the recovered group is considered thanks to some sufficient defense mechanisms or antivirus treatments; (c) the dysfunction of devices relates to natural death and depends on worm-related death, because in the real world, the crash of most devices results from the attack of malicious worms; and (d) the worm epidemic intervention strategies are established by reducing its size and speed. E rest of our paper is constructed as follows: in Section 2, we introduce the SEIQR-type model with saturated incidence rate; in Section 3, we analyze the stabilities of worm-free and worm-existence equilibria; in Section 4, we implement the numerical analysis and experiments; in Section 5, we identify the worm epidemic intervention strategies; in Section 6, we conclude and discuss the paper; and in Appendix section, we prove the main results obtained
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