Energy constraint hinders the popularization and development of wireless sensor networks (WSNs). As an emerging technology equipped with rechargeable batteries, wireless rechargeable sensor networks (WRSNs) are being widely accepted and recognized. In this paper, we research the security issues in WRSNs which need to be addressed urgently. After considering the charging process, the activating anti-malware program process, and the launching malicious attack process in the modeling, the susceptible–infected–anti-malware–low-energy–susceptible (SIALS) model is proposed. Through the method of epidemic dynamics, this paper analyzes the local and global stabilities of the SIALS model. Besides, this paper introduces a five-tuple attack–defense game model to further study the dynamic relationship between malware and WRSNs. By introducing a cost function and constructing a Hamiltonian function, the optimal strategies for malware and WRSNs are obtained based on the Pontryagin Maximum Principle. Furthermore, the simulation results show the validation of the proposed theories and reveal the influence of parameters on the infection. In detail, the Forward–Backward Sweep method is applied to solve the issues of convergence of co-state variables at terminal moment.

中文翻译：

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基于攻防博弈模型的无线充电传感器网络流行病分析

能量限制阻碍了无线传感器网络（WSN）的普及和发展。作为配备有可充电电池的新兴技术，无线可充电传感器网络（WRSN）已被广泛接受和认可。在本文中，我们研究了WRSN中的安全问题，这些问题亟待解决。在考虑了计费过程，激活的反恶意软件程序过程以及建模中的启动恶意攻击过程之后，提出了易受感染的反恶意软件-低能耗易感（SIALS）模型。通过流行病学方法，分析了SIALS模型的局部和全局稳定性。此外，本文介绍了一种五元组的攻击防御游戏模型，以进一步研究恶意软件与WRSN之间的动态关系。通过引入代价函数并构造哈密顿函数，基于庞特里亚金最大原理，获得了针对恶意软件和WRSN的最佳策略。此外，仿真结果表明了所提出理论的有效性，并揭示了参数对感染的影响。详细地，向前-向后扫描方法被用于解决终端时刻共态变量的收敛问题。