Dynamical Analysis and Control of a Connected Patch-Implantation-Driven Mobile Device System: A Fractional SVEIS Model Method

With the popularization of communication technology, mobile devices are conveniently used to transfer and obtain information. The resulting communication network security issues are drawing more and more attention. This study is dedicated to the modeling and optimal control problems for the malware propagation between mobile devices, in which the patch-implantation and device repair are considered. A fractional network-based SVEIS (Susceptible-Vaccinated-Exposed-Infectious-Susceptible) model is developed and investigated. Different from the previous malware propagation models, the considered transmission mechanism not only includes imperfect patch-implantation and reinfection after repair, but also incorporates the impact of memory effect. The next-generation matrix method is employed to obtain a critical threshold, which denotes the mean number of newly infectious devices resulting from an infectious device in a fully susceptible mobile devices environment. The existence and stability of the steady state are analyzed correspondingly to facilitate the control of malware. The cases where multi-equilibria coexist are also given in detail. Moreover, the optimal control strategy with respect to patch-implantation and repair is designed to trade off the infectious device prevalence and control cost. The proposed model provides a benchmark for patch-implantation and repair rate in a connected mobile device system. Finally, numerical simulations are conducted to assess the model’s effectiveness while investigating the sensitivity of its parameters in the context of a Barabási-Albert (BA) scale-free network. The control effects of various strategies are evaluated through comparative experiments. And a comparison with two established models is conducted to validate the enhanced risk assessment capabilities of the proposed framework.