A novel deterministic SEIS model for the transmission of email viruses in growing communication networks is formulated. Interestingly, the model is different from classical SEIS models not only in the form, but also in the dynamical features. We study the equilibria and their stability and analyse the bifurcation dynamics of the model. In particular, we find that the virus-free equilibrium is locally asymptotically stable for any parameter values, which may attribute to the absence of the basic reproduction number. It is shown that the model undergoes a saddle-node bifurcation and admits the bistable phenomenon. Moreover, on the basis of the Lyapunov function, the domains of attraction of equilibria are estimated by solving an LMI optimization problem. Based on the above theoretical results, some effective strategies are also provided to control the propagation of the email viruses. Additionally, our results are confirmed by numerical simulations.
Computer users’ reactions to the outbreak of Internet worm directly determine the defense capability of the computer and play an important role in the spread of worm. In this paper, in order to characterize the impacts of adaptive user protection behaviors, an improved SIS model is proposed to describe the Internet worm propagation. The results of theoretical analysis indicate that the protective campaigns of users can indeed reduce the worm’s reproduction number to values less than one. But it may not be sufficient to eradicate the worm. In certain condition, a backward bifurcation leading to bistability can occur. These are new findings in the worm propagation model that bring new challenges to control the spread of the worm and further demonstrate the importance of user behaviors in controlling the worm propagation. Corresponding to the analysis results, defense and control strategies are provided.
The effects of removable devices’ heterouse in different areas on the propagation of malware spreading via removable devices remain unclear. As a result, in this paper, we present a model incorporating the heterogeneous use of removable devices, obtained by dividing the using rate into local area’s rate, neighbour area’s rate and global area’s rate, and then getting the final rate by multiplying the corresponding area ratio. The model’s equilibria and their stability conditions are obtained mathematically and verified by deterministic and stochastic simulations. Simulation results also indicate that the heterogeneity in using rate significantly changes the prospective propagation course of malware. Additionally, the thresholds of removable devices’ using rate in neighbour area are given, which can guide us in designing effective countermalware method.
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