Exploring the Dynamics of a Malware Propagation Model and Its Control Strategy

An e-epidemic SIRS (susceptible-infected-recovered-susceptible) model is proposed with a generalized non-monotone incidence rate characterizing the psychological effect of some devastating malware when the number of infected nodes are getting larger. Existence of unique and multiple equilibria, linear and non-linear stability with the help of basic reproduction number, and the nature of temporal system dynamics are analyzed. Bifurcation analyses (backward and forward transcritical bifurcation, Hopf bifurcation) are performed that are exhibited by the temporal system. It has been shown that saturation recovery of infected nodes along with the malware transmission rate lead to vital dynamics such as monostable and bistable, when basic reproduction number ( $$R_0$$ ) is less than unity. Further, state feedback controller is introduced along with the time delay for extending the region of stability and delaying the occurrence of Hopf bifurcation in the network. All the analytical results are validated through numerical simulation experiments. Numerically, it reflects that a larger value of inhibition factor, a and smaller value of $$\gamma $$ can accelerate the malware removal and reduces the infection level in the network. Our study helps to understand how the psychological effect impacts on the network malware propagation process. The analysis and simulation results are useful for the policy-making insights of the anti-malware practices in the information sharing networks.