Spatiotemporal Optimal Control of Malware Propagation in AUV-Assisted UWSNs: A Two-Layer Heterogeneous Network

Autonomous Underwater Vehicle (AUV)-assisted Underwater Wireless Sensor Networks (UWSNs) offer transformative potential for data collection, disaster prediction and environmental monitoring. However, these networks remain critically vulnerable to malware attacks due to inherent communication challenges and limited energy resources. To rigorously capture the spatiotemporal dynamics of malware propagation, this paper introduces a novel two-layer heterogeneous model rooted in Partial Differential Equations (PDEs). To suppress malware propagation under limited bandwidth, this paper proposes a spatiotemporal optimal control strategy integrating saturation functions. The existence of the optimal pair is demonstrated by the minimizing sequence method, and the first-order necessary condition for spatiotemporal control is derived based on convex perturbation methods. Further, extensive numerical experiments validate the effectiveness of the proposed two-layer heterogeneous model and spatiotemporal control strategy. Finally, the applications of the proposed model and control strategy in real-world scenarios are discussed.