Study Of Some Classes Stochastic Epidemic Models With Information Intervention

In the real environment,the occurrence and spread of infectious diseases are inevitably affected by many unpredictable environmental noise.Therefore,the introduction of random interference in the infectious disease model will be closer to the reality and have more practical biological significance.This paper mainly considers the influence of environmental noise on epidemic models,and establishes new stochastic epidemic models.The paper is divided into five chapters:The first chapter introduces the research background and main work,as well as the prepara-tory knowledge used in this paper.In chapter 2,on the basis of the model studied in the literature,considering that the trans-mission rate of the disease and the recovery rate of the infected are affected by the environmental noise.A new stochastic SIRS epidemic model with information intervention is established.First-ly,by establishing the appropriate Lyapunov function and using the Ito's formula,it is proved that the stochastic model has a unique global positive solution.The sufficient conditions for disease extinction and persistence are obtained by using the strong law of numbers and other methods.Through numerical simulation,it is shown that although the disease is persistent in the deterministic model,the high intensity of white noise in the environment will still lead to disease extinction.This shows that environmental noise can suppress the outbreak of disease.In chapter 3,based on the stochastic epidemic model established in the second chapter,another new stochastic SIRS epidemic disease model with information intervention is established.Firstly,similar to the method in the second chapter,we get the unique global positive solution of the new stochastic system,as well as the extinction and persistence of the disease in the model.Then the existence and uniqueness of the stationary distribution of the stochastic system is proved by using the Khasminskii method.Finally,the conclusion is verified by numerical simulation.In chapter 4,based on the model of waterborne pathogens discussed by predecessors,the corresponding stochastic waterborne pathogens model is established.Firstly,by using the s-tochastic Lyapunov function and the Ito's formula,the unique global positive solution of the stochastic model is proved.The sufficient conditions for the extinction and persistence of disease are obtained by using the strong law of numbers and other methods.Then the sufficient condi-tions for the existence of stationary distribution of stochastic system are obtained by using the Khasminskii method.Finally,the results of this chapter are verified by numerical simulation.In chapter 5,summarizes the main results of this study and looks forward to the future research work.