Analytical Optimal Control of Delayed Worm Propagation Model in Heterogeneous IoT Systems

This paper presents a mathematical model for worm propagation, where infectivity is influenced by latency within heterogeneous Internet of Things (IoT) systems. The model incorporates the heterogeneity of susceptible-exposed-infected-recovered (SEIR) compartments and considers the varying negative impacts of worms spread across these groups. Sufficient conditions for the persistence of worm propagation are derived using the optimistic equilibrium point. By selecting latency as a bifurcation parameter, the study reveals a specific latency value critical for maintaining worm propagation’s stability in these systems. The normal form approach and central manifold theory are employed to analyze the direction and stability of Hopf bifurcation. Furthermore, this study addresses strategies for mitigating the spread of worms by employing best practices to minimize the number of devices exposed and infected across systems. We analyze the effects of control measures, such as vaccination and treatment, which should be applied promptly during a worm proliferation outbreak and gradually scaled down over time as the outbreak decreases. Numerical findings expose that latency significantly impacts system stability, however, optimally managing the latency below a deterministic threshold may maintain system stabilization.