Differential Games of Rechargeable Wireless Sensor Networks against Malicious Programs Based on SILRD Propagation Model

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