A Novel Epidemic Model Base on Pulse Charging in Wireless Rechargeable Sensor Networks

As wireless rechargeable sensor networks (WRSNs) are gradually being widely accepted and recognized, the security issues of WRSNs have also become the focus of research discussion. In the existing WRSNs research, few people introduced the idea of pulse charging. Taking into account the utilization rate of nodes' energy, this paper proposes a novel pulse infectious disease model (SIALS-P), which is composed of susceptible, infected, anti-malware and low-energy susceptible states under pulse charging, to deal with the security issues of WRSNs. In each periodic pulse point, some parts of low energy states (LS nodes, LI nodes) will be converted into the normal energy states (S nodes, I nodes) to control the number of susceptible nodes and infected nodes. This paper first analyzes the local stability of the SIALS-P model by Floquet theory. Then, a suitable comparison system is given by comparing theorem to analyze the stability of malware-free T-period solution and the persistence of malware transmission. Additionally, the optimal control of the proposed model is analyzed. Finally, the comparative simulation analysis regarding the proposed model, the non-charging model and the continuous charging model is given, and the effects of parameters on the basic reproduction number of the three models are shown. Meanwhile, the sensitivity of each parameter and the optimal control theory is further verified.