Analysis Of Hepatitis B Epidemic Model With Vaccination

Hepatitis B is a chronic hepatitis infection caused by a DNA virus.According to statistics from the World Health Organization,at the end of 2015,there were more than 300 million hepatitis patients in the world,and 257 million hepatitis B infected patients.There are 71 million people infected with hepatitis,and the global burden of chronic hepatitis is nearly 50%.It is concentrated in developing countries such as China and Brazil.In order to prevent and treat hepatitis B infectious diseases,many countries have invested a lot of funds for medical research.This article based on the transmission mechanism of hepatitis B,As well as the prevention and treatment strategies that have been implemented,construct a mathematical models for the study of hepatitis B infectious diseases.In the first chapter,we first introduced the background knowledge of hepatitis B,including the clinical characteristics of patients with hepatitis B infection,the impact on global human health,the characteristics and transmission mechanism of hepatitis B virus,and current medical treatment and prevention of hepatitis B infection.Then some research advances in the mathematical modeling of hepatitis B infectious diseases through vaccination are introduced.At last,some related mathematical theorems used in this paper are given.In Chapter 2,we consider an epidemic model of HBV with the effects of vaccinal effectiveness and latency.First,the existence of equilibria is discussed.Then,the basic reproduction number R0 is computed,we obtain that the system still exists a virus-free equilibrium,and there is a unique endemic equilibrium when R0>1.Finally,we prove the global stabilities of the virus-free equilibrium and endemic equilibrium by constructing Lyapunov functions.In Chapter 3,we consider that carriers of hepatitis B virus do not show long-term morbidity,but they are susceptible to infection.Based on the original model,we added a type of virus carrier C and considered that the infected person and the viral carrier would jointly transmit the disease,establish a new model,and determine the basic reproductive number,disease-free balance point,and positive balance point of the system.The Lyapunov function proves that whenR1<1,R 2<1,there is a unique positive equilibrium and it is globally stable;when R0>1,there is a globally asymptotically stable positive equilibrium.In the last chapter,we review the conclusions of this paper,and put forward some issues that are worthy of concern for hepatitis B infectious diseases in order to guide the direction of future work.