Dynamic Behaviors Of Two Types Of Age Structured Epidemic Models

With the outbreak of COVID-19 all over the world in 2020,the research on infectious disease model has become a hot topic again.The study of the model with age structure is one of the important topics in the dynamics of infectious diseases.In this paper,we use the linear operator semigroup theory,spectral analysis method and the theory of infinite dimensional dynamic system to study the dynamic behaviors of two kinds of age structured models.For the infection model with long disease duration,considering the long-term latent characteristics of the disease,that is,the patients in the latent period also have the ability to infect susceptible person.In the second part,we introduce a delay term and establish an age structured SIR model with time delay.In this paper,we first establish a Banach space for this model,and then we analyze the existence and uniqueness of the solution,the local asymptotic behavior and the global behavior of the steady-state solution of the SIR model with time-delay age structure by using the spectral analysis theory.In the third part,for the classical SIR model with nonlinear incidence,we introduce the age of infection to study the dynamic behavior of SIR model.The existence of solutions is proved by using the theory of strongly continuous semigroups.The asymptotic stability of steady-state solution of SIR model with nonlinear incidence and infection age is studied by spectral analysis theory.In particular,we prove that the solution is uniformly persistent by the existence of global attractor.