Analysis of Time-Delay Epidemic Model in Rechargeable Wireless Sensor Networks

Abstract

With the development of wireless rechargeable sensor networks (WRSNs), many scholars began to attach attention to network security under the spread of viruses. This paper mainly studies a novel low-energy-status-based model SISL (Susceptible, Infected, Susceptible, Low-Energy). The conversion process from low-energy nodes to susceptible nodes is called charging. It is noted that the time delay of the charging process in WRSNs should be considered. However, the charging process and its time delay have not been investigated in traditional epidemic models in WRSNs. Thus, the model SISL is proposed. The basic reproduction number, the disease-free equilibrium point, and the endemic equilibrium point are discussed here. Meanwhile, local stability and global stability of the disease-free equilibrium point and the endemic equilibrium point are analyzed. The addition of the time-delay term needs to be analyzed to determine whether it affects the stability. The intervention treatment strategy under the optimal control is obtained through the establishment of the Hamiltonian function and the application of the Pontryagin principle. Finally, the theoretical results are verified by simulations.