Virus spreading problems in wireless rechargeable sensor networks (WSNs) are becoming a hot topic, and the problem has been studied and discussed in recent years. Many epidemic spreading models have been introduced for revealing how a virus spreads and how a virus is suppressed. However, most of them assumed the sensors are not rechargeable sensors. In addition, most of existing works do not consider virus mutation problems. This paper proposes a novel epidemic model, including susceptible, infected, variant, low-energy and dead states, which considers the rechargeable sensors and the virus mutation factor. The stability of the proposed model is first analyzed by adopting the characteristic equation and constructing Lyapunov functions methods. Then, an optimal control problem is formulated to control the virus spread and decrease the cost of the networks by applying Pontryagin’s maximum principle. Finally, all of the theoretical results are confirmed by numerical simulation.

中文翻译：

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用于病毒变异传播的无线充电传感器网络的动力学分析

无线可充电传感器网络（WSN）中的病毒传播问题正成为一个热门话题，并且近年来对该问题进行了研究和讨论。已经引入了许多流行病传播模型，以揭示病毒如何传播以及如何抑制病毒。但是，大多数人都认为传感器不是可充电传感器。此外，大多数现有的工作都没有考虑病毒突变问题。本文提出了一种新的流行病模型，该模型包括易感性，感染性，变异性，低能状态和死亡状态，其中考虑了可充电传感器和病毒突变因素。首先通过采用特征方程并构造Lyapunov函数方法来分析所提出模型的稳定性。然后，通过应用庞特里亚金的最大原理，制定了一个最优控制问题来控制病毒传播并降低网络成本。最后，所有的理论结果都通过数值模拟得到了证实。