Propagation dynamics of malware in wireless sensor networks with node sleep-active scheduling based on simplicial complexes

Abstract Traditional studies of malware propagation in wireless sensor networks (WSNs) have predominantly focused on pairwise interactions. However, real-world contagion processes often involve higher-order interactions, in which multiple nodes jointly participate in infection events. To capture such group-based dynamics, this study proposes a malware propagation model that features higher-order interactions and node sleep-scheduling. Within the framework of the quenched mean-field (QMF) theory, we derive the node probability evolution equations and employ the mean-field (MF) approximation to obtain the two malware propagation thresholds related to bistability, together with the existence and stability conditions of the equilibrium points. Theoretical analysis reveals that the pairwise infection rate can induce the emergence of bistability. Furthermore, a Sobol-based sensitivity analysis is conducted to quantify the influence of each model parameter on the persistent propagation threshold, and the results indicate that the transition rates between sleep and active states together with the average degree of pairwise interactions play a dominant role in determining the persistent propagation threshold. The numerical simulations show that increasing the node activation rate, or decreasing the sleep rate, can induce a transition from a forward to a backward bifurcation, leading to bistability in which malware may either vanish or persist depending on the initial infection level.