| Infectious diseases have always been the great enemies to human health.Throughouthistory, infectious diseases brought great disaster to human survival and livelihood againand again. So the subject of researching infectious diseases model has its scientific value. Using the infectious disease model to study the spread of infection rule in mathematicswill help infectious disease control and prevention.With the deep studies of the epidemicmodel, We discovered some epidemic characteristics, for example, some epidemic haslonger disease infection time, so we should consider age-structured. Besides, when usingthe vaccination to prevent some epidemics, the protection function of the vaccine woulddisappear or be weakened gradually along with the increase of time, that is non-lifelongimmunity. By using the partial diferential equation system with vaccination to researchwould make this kind of epidemic model with age-structured matched some actual mean-ing more.The paper studied an age-structured and vaccination SEIRS epidemic model, themain contents can be summarized as follows:1. In section one, firstly, we introduce the important value of epidemic mathematicalmodels. Then, the development of epidemic mathematical model is summarized, andthe research presents condition of infectious disease model with an age-structured andvaccination, finally we introduced the main contents in this paper.2. In section two, the well-posedness of SEIRS model 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 three, the model in this paper summarize and discuss still can continueof research. |
