Epidemic Analysis of Wireless Rechargeable Sensor Networks Based on an Attack–Defense Game Model

Abstract

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.

Modelling and Analysis of the Epidemic Model under Pulse Charging in Wireless Rechargeable Sensor Networks

“…However, with the development of the Internet of Things (IOT) industry, heterogeneous network technology has become mainstream, and the pulse charging strategy for the heterogeneous network is one of our future research directions. Additonally, some impulsive models can be extended into depict the dynamics of infectious disease based on the security problem of WRSNs [15] in future.…”

“…, where Φ (0) = E 0 (E 0 is the identity matrix), obtained by Equation ( 12), Equation ( 14) and system (15), we can obtain the following matrix…”

“…For example, Wang et al [14] proposed an effective and efficient immunization strategy for MWSNs based on pulse differential equations and the SIR model. Similarly, Liu et al proposed an optimal control scheme based on the novel epidemic model (SILS) [15], and Cao et al obtained the optimal control variables of immunization ratio and recovery ratio by using Pontryagin's maximum principle based on the theory of infectious disease [16].…”

Dynamics Analysis of a Wireless Rechargeable Sensor Network for Virus Mutation Spreading

“…Cao et al [16] considered the recovered factor to construct the model of WSNs, and the authors patched the dissemination of security and immunized or healed the nodes to use the security strategy; Zheng et al [17] considered the vaccination strategies with temporary immunity and a quarantined strategy to construct an SEIQR model; Han et al [18] considered the system of the nonlinear stochastic system to construct an SEIR model. Liu et al [19] considered the low-energy factor to construct a model of WRSNs, and the stability of the model was proved. According to Liu et al [19][20][21][22], the system is a good combination of an epidemic dynamic model and wireless sensor network.…”

“…Liu et al [19] considered the low-energy factor to construct a model of WRSNs, and the stability of the model was proved. According to Liu et al [19][20][21][22], the system is a good combination of an epidemic dynamic model and wireless sensor network. Thus, the system skillfully blends the information of the WRSNs with biological characteristics.…”