Dynamic Analysis Of Stochastic Epidemic Model On Networks

During the spread of the disease,the structure of contact networks plays a crucial role.Therefore,complex networks have been widely studied for their applications in dynamics of infectious diseases.In addition,the spread of infectious diseases is often affected by random environments.The stochastic epidemic model on complex networks can more reasonably describe the spreading process of epidemic.Based on this,this thesis will establish two types of stochastic epidmic models on complex networks and analyze their dynamic behavior.Chapter 1 mainly introduces the domestic and foreign researches trends of establishing stochatic epidemic model on complex networks.It describes the common types of epidemic model,and explains the rationality of establishing a stochastic epidemic model on complex networks.Finally,the definitions and theorems used in this thesis are given.Chapter 2 builds a stochastic SIS model on complex networks.Firstly,by constructing a suitable Lyapunov function and stopping time,existence and uniqueness of global positive solutions of this model are proved.Secondly,using the theory of stochastic stability,the conditions for the global stochastic asymptotic stability of the zero solution are proved,and according to the Ito's formula and Chebyshev's inequality,the stochastic persistence conditions of the model are proved.Finally,numerical simulation proves the rationality of the theoretical results.Meanwhile,it can be seen from the numerical simulation,the noise intensity can affect the intensity amplitude of infectious diseases.Chapter 3 builds a stochastic SAIS model on complex networks.Firstly,use the ex-istence and uniqueness theorem of local solutions of stochastic differential equations and Lyapunov function to prove the existence and uniqueness of the global positive solutions of this model.Secondly,using the theory of stochastic stability,the conditions for the global stochastic asymptotic stability of the zero solution are proved.Then,constructing a suit-able Lyapunov function and Chebyshev's inequality,the persistence conditions of disease are proved.Finally,numerical simulation proves the rationality of the theoretical results.Numerical simulation shows that the greater the noise intensity,the greater the vibration amplitude of the solution of the stochastic model around the positive equilibrium point of the deterministic model.Finally,the stochastic epidemic model established in this thesis and its theoretical analysis results are summarized,and the next research content is given.