Persistent Solutions Of A Stochastic Epidemic Dynamic Equation With Vaccination

Infectious diseases have always threatened human health and life.Establishing a dynamic model is an effective method to study infectious diseases.By studying the dynamic properties of the model,we can understand the development process of infectious diseases,predict the epidemic rules and trends,and seek the optimal prevention and control strategies.In the real world,it is inevitable to be affected by environmental noise.At this time,the deterministic epidemic model is not always ideal.In order to better reflect the situation in the real world,it is particularly necessary to study the epidemic model affected by random factors.Vaccination is considered to be an important means to eliminate infectious diseases.Vaccination can improve the level of immunity and prevent and inhibit the spread of diseases.Based on this background,this paper proposes a stochastic epidemic dynamic model affected by vaccine factors,analyzes the dynamic properties of model,and provides scientific theoretical basis for the prevention and control of infectious diseases.The specific research work is as follows :The first chapter mainly introduces the development history of infectious diseases,the research status of epidemic dynamic model at home and abroad,the research background and significance,and the main structure of this paper.In the second chapter,the epidemic model part introduces the classical epidemic model,briefly describes the relevant concepts,dynamic basis,and defines the basic knowledge used in the article.The third chapter is about the persistent solution of the stochastic SIRV epidemic model influenced by vaccines.On the basis of the classical SIRS epidemic model,a class of vaccine-influenced epidemic model is developed by considering the effect of vaccination,and a stochastic perturbation term is introduced to obtain a stochastic SIRV epidemic model by considering the effect of environmental noise.Based on the theory of stochastic differential equations,the global non-negativity of the model solution is proved and the persistent solution of the model is investigated,which is finally validated by numerical simulations using the Milstein method.The fourth chapter is about the asymptotics of the stochastic SIRV epidemic model influenced by vaccines.A brief conclusion on the asymptotics of the model is obtained using stochastic differential equation theory in the case of weakening the independence between perturbations in the model and validated with numerical simulations.