Based on the traditional propagation model, this paper innovatively divides nodes into high- and low-energy states through\nintroducing Low-energy (L) state and presents a whole new propagation model which is more suitable for WSNs (wireless sensor\nnetworks) against malicious programs, namely, SILRD (Susceptible, Infected, Low-energy, Recovered, Dead) model. In this paper,\nnodes are divided into five states according to the residual energy and infection level, and the differential equations are constructed\nto describe the evolution of nodes. At the same time, aiming at the exhaustion of WSNsâ?? energy, this paper introduces charging as a\nmethod to supplement the energy. Furthermore, we regard the confrontation between WSNs and malicious programs as a kind of\ngame and find the optimal strategies by using the Pontryagin Maximum Principle. It is found that charging as a defense\nmechanism can inhibit the spread of malicious programs and reduce overall costs. Meanwhile, the superiority of bang-bang\ncontrol on the SILRD model is highlighted by comparing with square control.
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