Dynamical Behaviors Of Two Classes Of Stochastic Epidemic Models

The wide spread of epidemic will inevitably bring great threat and influence to human health,economy and social progress.Epidemic dynamics analysis method is one of the most effective methods to study the characteristics and laws of epidemic transmission.This paper establishes a mathematical model that can accurately describe the characteristics of epidemic transmission,and studies the dynamic behavior of the model through various mathematical theories and methods.The results provide a theoretical basis for the prevention and control of the occurrence and spread of the epidemic.Therefore,the study of epidemic dynamic model has certain research significance and application value.Considering the random interference and uncertainty of various factors in the environment,it will inevitably affect the transmission process of the epidemic,It is more practical to add random disturbance to epidemic dynamics model.Therefore,this paper studies the dynamic behavior of stochastic oncolytic therapy model and stochastic cholera model by using epidemic dynamics method and stochastic differential equation theory.The first chapter introduces the research background and significance of oncolytic therapy model and cholera model,and gives some basic definitions and preparatory knowledge related to this paper.In Chapter 2,we study the dynamic behavior of a stochastic oncolytic therapy model with Logistic growth;Secondly,it is proved that the stochastic oncolytic therapy system has asymptotic behavior at the disease-free equilibrium and endemic equilibrium of its deterministic system when the model parameters satisfy certain conditions;Finally,the correctness of the theoretical analysis results is verified by numerical simulation.In Chapter 3,we study the dynamic behavior of a stochastic model for cholera treatment by isolation;Furthermore,through the theory of stochastic differential equations,we construct an appropriate Lyapunov function,and prove the asymptotic behavior of the stochastic cholera model at the disease-free equilibrium and endemic equilibrium of its deterministic system by using It?’s formula.Finally,numerical simulation is used to verify the theoretical results.The fourth chapter summarizes this paper,and points out the shortcomings of this paper and the next research work...