Analysis Of Epidemic Model With Vaccination And Age Structure

From the long-term spread of measles to the outbreak of COVID-19 in the past two years,the health of human is under the dire threat of infectious diseases.Prevention and control of disease is an important problem which should be paid much attention to,and vaccination is one of the key means of disease prevention and control.Based on epidemiological characteristics of measles and COVID-19,the thesis establishes the infectious disease model with continuous,pulse vaccination and age structure.The effects of vaccination methods,vaccination ages and the possibility of immune regression on the spread of the disease is investigated,and valuable suggestions for the actual control of measles and COVID-19 transmission is provided through numerical simulation.In chapter 2,an age structure model with latent infection and vaccination is established,which takes into account the great challenges posed by latent infection to disease prevention and control.Firstly,the existence of disease-free equilibrium and endemic equilibrium are discussed,and the expressions of the effective reproduction number and the basic reproduction number are obtained.Then the global asymptotic stability of the disease-free equilibrium is proved by using Lyapunov indirect method and the method of characteristic line,and the local asymptotic stability of endemic equilibrium is obtained.Furthermore,based on the original model,an age-structured COVID-19 transmission model with latent infection and limited vaccine resources considering the COVID-19 vaccination situation is established.Finally,the effective reproduction number is used as the measurement value to explore the optimal vaccination strategy under the background of the early spread of COVID-19 in Wuhan through numerical simulation.The study finds that the optimal vaccination age is closely related to incidence.In chapter 3,according to the epidemiological characteristics of measles and the situation of vaccine immunity,an age structure model with pulse vaccination,maternal antibody and secondary vaccine failure is established.Firstly,the expression of the effective reproduction number and the existence of disease-free equilibrium are obtained,and the existence and uniqueness of endemic equilibrium point is discussed.Secondly,the global stability of disease-free equilibrium is proved.Finally,a numerical simulation is conducted according to the real datum of infection cases aged 0-10 years in China during 2005-2019,which implies that vaccination age and vaccination rates affect the effectiveness of disease prevention and control.