Modeling and Stability Analysis of Malware Propagation in Hierarchically Protected WSNs Based on Epidemiological Theory

ABSTRACT Wireless sensor networks (WSNs) are highly vulnerable to malware attacks due to resource constraints. However, existing propagation models often overlook the heterogeneous security levels in hierarchically protected WSNs, leading to inaccurate representations of dynamics across network layers. This paper proposes a novel malware propagation model specifically for hierarchically protected WSNs to capture the distinct defense capabilities of heterogeneous nodes. Based on epidemiological theory, nodes are stratified into high protection level (HPL) and low protection level (LPL) categories within a susceptible‐exposed‐infected‐recovered (SEIR) differential equation framework. We rigorously derive the basic reproduction number () and prove the global asymptotic stability of equilibrium points using Lyapunov function analysis. Theoretical and experimental results demonstrate that malware is eradicated when , whereas it persists endemically when . Specifically, simulations reveal that while HPL nodes exhibit lower infection rates, their compromise significantly accelerates network‐wide propagation due to high connectivity. Furthermore, a critical communication radius threshold is identified; exceeding this threshold triggers a transition to an endemic state. The proposed model offers theoretical insights for defense strategies, suggesting that optimizing the HPL node proportion and regulating communication radius are critical for mitigating malware propagation.