Research On Age-structured Epidemic Models

This paper has studied the age-structured epidemic models.The main purpose of establishing infectious disease model is to use the model to descript the biology and sociology mechanism which influent the spread of infectious disease. And then we can reveal the infect rule by studying the model. And also we can forecast the infect trend to provide the basis and strategy for discovering, preventing and controlling the infectious disease.We establish 3 epidemic models with age-structured according to the difference of the diseases. They are:An SEIQR model with age-structured and isolation; An HFMD model with age-structured; An SIR model with immigration.They are all partial differential equations (PDE). We analyze the models'characters using the related theory of epidemic dynamics and the related theory of real variable function. We find the condition of die out or exist when disease happens. When the basic reproductive number is less than one, the disease-free equilibrium exists uniquely and it is local asymptotically stable (or global asymptotically stable). When the basic reproductive number is above one, it is proved that both the disease-free equilibrium and the endemic equilibrium exist, the disease-free equilibrium is unstable and the endemic equilibrium is local asymptotically stable under some conditions (or the characteristic equation of the nonlinear system in the endemic equilibrium has no nonnegative real root).Finally, based on the above theoretical results, we simulate the models'solutions, and obtain the difference format of the models with numerical method. And then, we program the format in Matlab. In the end, we simulate the develop trend of susceptible and infected. In order to fine the factors that affect the result, we change the parameters of the models when doing the computer test. This can provide a good foundation for the practice.Experimental results show that, the two equilibrium of the model are linked to basic reproductive number closely. And the basic reproductive number relies on the parameters in the models. So we can control the spread of infectious diseases by controlling some parameters.The innovation of this thesis is that we use the methods of epidemic dynamics to the age-structured epidemic models successfully, and we analyze the endemic equilibrium in deeper level.