The Research And Application Of Several Stochastic Hepatitis B Models

Viral hepatitis is one of the common infectious diseases that seriously affect people's health in China.According to the types of virus infection,it can be divided into viral hepatitis A,B,C,D and E.Among them,hepatitis B has the highest infection rate and the greatest harm.HBV can be transmitted through mother to child,blood and blood products,damaged skin and mucous membrane and sexual contact.In this case,the World Health Organization proposed that hepatitis B vaccination is the main measure to prevent hepatitis B.Based on this,this paper studies the dynamics and applications of several stochastic hepatitis B models.The content is as follows:In chapter 1,It briefly introduces the biological background and significance of studying the hepatitis B model,and gives the relevant knowledge needed in this article.In chapter 2,a deterministic model of hepatitis B with vaccination and mother to child transmission is established.The threshold R0 is given to determine whether hepatitis B is prevalent or not.The dynamic behavior of the deterministic model is proved by using La Salle's invariance principle and Dulac judge theorem.Then,due to the continuous fluctuation of the environment,it is assumed that the disease transmission coefficient ? will fluctuate around the average value.Therefore,randomization was introduced into the previously established deterministic model to obtain a stochastic model of hepatitis B with vaccination and mother-to-child transmission.The Lyapunov function is constructed to prove the existence and uniqueness of the global positive solution.The threshold ?R0that determines the extinction and persistence of hepatitis B is given,and the necessary and sufficient conditions for the extinction and persistence of hepatitis B are proposed.Finally,based on the background of hepatitis B prevention measures in China,we will use deterministic model and stochastic model for numerical simulation to show the effectiveness of hepatitis B prevention measures.In chapter 3,a stochastic model with vaccination and delay is established.First,we prove that the solution of the system is globally unique,positive,and stochastically bounded.Then,construct the Lyapunov function to study the stochastic stability of the system at the disease-free equilibrium.In addition,the threshold ?R0that determines the extinction and persistence of the disease is given.Furthermore,we study the ergodicity of the model and the existence of a stationary distribution,which will help us better understand the dynamic behavior and statistical distribution characteristics of a stochastic time-delay epidemic model.Finally,we applied the results to hepatitis B in China's mainland.The parameters are estimated using the nonlinear square method,and the threshold ?R0= 0.0556 is obtained.We predict that the number of people infected with hepatitis B in China's mainland will drop from90 million in 2015 to about 20 million in 2100,and give the probability density of hepatitis B infection each year.In short,this article established a hepatitis B model with factors such as vaccination,time lag,mother-to-child transmission,and different environmental disturbances.Analyzed the effectiveness of hepatitis B prevention measures in China,predicted the changes in the number of hepatitis B infections in China,and finally summarized the work,and proposed the next step of research and the goal of efforts.