Modeling And Analysis Of Wireless Rechargeable Sensor Networks Based On Infectious Disease Dynamics

With the continuous development and application of Wireless Sensor Networks(WSNs)technology into daily life,industry,agriculture,manufacturing and other fields,problems such as limited energy and information security in WSNs have been paid close attention and studied by the academic community.Wireless Rechargeable Sensor Networks(WRSNs)technology uses mobile chargers such as Unmanned Aerial Vehicles(UAVs)and autonomous vehicles to charge the sensor nodes in the networks.While WRSNs solves the energy bottleneck of the networks,it is equally urgent and important to solve its security problem.Generally speaking,the research on WRSNs focuses on energy optimization and schedulings and the discussion on its security focuses on improving the security and reliability of data communication.Through the construction of the novel epidemic models,this thesis takes WRSNs as the research object,study the confrontation between malware and WRSNs and analyze the propagation roles of malware in WSRNs by using the method of differential game theory and epidemic dynamics.By considering the residual energy of sensor nodes in WRSNs,dividing the sensor nodes in the network into high energy sensor nodes and low energy sensor nodes is the basis of modeling in this paper As a characteristic of WRSNs,charging the sensor nodes in the network is also one of the modeling features in this thesis.The first part of the main content of this thesis is based on the SIR(Susceptible-InfectedRecovered)model.With the consideration of charging,a novel model,namely SILRD(Susceptible--Infected--Low-energy--Recovered--Dead),is put forward innovatively.Furthermore,the dynamic game model between WRSNs and malware is constructed by using the principle of differential game,and the dynamic optimal strategies is solved by using the Maximum Principle.Finally,the effectiveness of the optimal control is verified by simulation and the advantages of Bang-bang control are analyzed by constructing different control combinations.In the second part of this thesis,we consider the security of Energy-Harvesting Wireless Sensor Networks(EHWSNs).Compared with the SILRD model in the first part,the study in the second part introduced concepts such as solar charging,nonlinear infection rate and multiple rounds of malware attacks,and proposed the ASILRD model suitable for EH-WSNs.Similarly,the dynamic optimal strategies between EHWSNs and malware is obtained by using the principle of differential game.Finally,in the simulation section,not only the optimality of the proposed strategy is verified,but also the influence of different charging ways,controllable and uncontrollable inputs,and different nodal degrees on the optimal control strategy are discussed.In the third part of this thesis,WRSNs with self-healing sensor nodes are took into consideration and the SILS(Susceptible--Infected--Low-energy--Dysfunctional)model is proposed.Firstly,the disease-free equilibrium and epidemic equilibrium of SILS model are obtained,and the basic regeneration number R0 of SILS model is obtained by using the nextgeneration matrix method.Then,by the method of stability analysis,the local and global stability of the disease-free equilibrium and the epidemic equilibrium are obtained respectively when R0<1 and R0>1.Then,the dynamic optimal control strategies between WRSNs and malware is analyzed by using the method of differential game.Finally,the stability of SILS model is verified further by simulation when R0<1 and R0>1,and the relationship between charging rate in SILS model,and the number of infected nodes and basic regeneration number R0 is analyzed.At the same time,the optimal control strategy is compared with nonoptimal control strategy to verify its effectiveness under the situation of R0<1 and R0>1.The fourth part of this thesis further details the repair process after the sensor nodes are infected with malware and puts forward the SIALS(Susceptible--Infected--Anti-malwareLow-energy--Dysfunctional)model.Like the third part,the disease-free equilibrium and epidemic equilibrium in the SIALS model are calculated and the local and global stability of the two equilibria are proved.Then,using the principle of differential game,we analyze the optimal strategies of WRSNs and malware.Finally,in the simulation section,the stability of the model and the optimality of the optimal strategy further verified.By introducing the concepts of low-energy state and charging,this thesis constructs four different epidemic models and analyzes their optimal control strategies and stability.In the last chapter,we summarize the whole work of the thesis and put forward some ideas for the future work.