The Study Of SEIR Epidemic Model With Age And Course Of Diseases

The spreading of the epidemics brings heavy calamity to human, and becomes one ofthe most valuable subjects for researchers no matter in home and abroad. The law of theepidemics'spreading is studied by the research of epidemic mathematical models,whichwill contribute to controlling and preventing the epidemics . In this paper, based on theresearches of other authors, we research a class of SEIR epidemic model with age andcourse of diseases. The main contents in this paper can be summarized as follows:1. In section 1, firstly, we introduce the important value of the research of epidemicmathematical models. Then, the development of the epidemic mathematical mode issummarized. Finally, the organization of this paper is also presented.2. In section 2, The well-posedness of model(2.1-2.2) is given. The existence anduniqueness of local solution is proved by characteristic method, the theories of integralequation and Banach fixed point theorem. Then the existence and uniqueness of globalsolution and continuous dependence of solution for initial value are obtained by priorestimation and Gronwall inequality. In the end, the regularity of solution is discussed.3. In section 3, The asymptotical behavior is analyzed for a special case of model(2.1-2.2).The existence of disease-free equilibrium and endemic equilibrium are proved. We getthe threshold (0) and prove that the disease-free equilibrium is globally asymptoticalattractor if (0) < 1.