Stability and Hopf bifurcation analysis of a delayed malware mutation model for wireless rechargeable sensor networks with energy constraints

With the rapid progression in the field of information technology, the security of wireless sensor networks (WSNs) becomes an alarming issue around the globe. This research presents an innovative malware propagation model for wireless rechargeable sensor networks (WRSNs), including virus mutation and two specific temporal delays: a charging delay (ς1) and a temporary vaccination period delay (ς2). In contrast to other models, our proposed approach accurately reflects the real-time dynamics of energy-constrained WRSNs by incorporating a fifth compartment for low-energy nodes and implementing unidirectional malware mutation. Utilizing linear stability and Hopf bifurcation analyses, we establish explicit criteria for the system's transition from stability to periodic oscillations. The incorporation of delay parameters clarifies essential thresholds for the occurrence of Hopf bifurcation. In contrast to Liu et al. (2020), who focused solely on charging delay and omitted global stability analysis, our enhanced model integrates two fundamental reproduction numbers, energy limitations, and dual delays, thereby facilitating more precise prediction and control of malware propagation. We additionally demonstrate global stability utilizing a Lyapunov functional and support our theoretical results with extensive numerical simulations. A stepwise implementation algorithm is also included to facilitate realistic deployment in IoT contexts. Our technique, in comparison to previous models, provides a delay reduction of up to 35%, increased resilience against mutated malware, and prolonged sustainable operation under energy limitations, rendering it extremely suitable for safe real-world WRSNs.