The Study On Age-structured And Impulsive Vaccination SEIRS Epidemic Model

With the deep studies of the epidemic model, We discovered some epidemic charac-teristics, for example, some epidemic has longer infection times, so we should considerpeople's age-structured. Expect that, when using the vaccination to prevent some epi-demic, the protection function of the vaccine would disappear or weaken gradually alongwith the increase of time, that is non-lifelong immunity. Used the partial di?erentialequation system with impulsive vaccination to research would make this kind of epidemicmodel with age-structured matched some actual meaning more.The paper studied an age-structured and impulsive vaccination SEIRS epidemicmodel, the main contents can be summarized as follows:1. In section one, we firstly introduce the background, purpose and meaning of study-ing infectious disease. Then, We introduced the research present condition of infectiousdisease model with an age-structured and impulsive vaccination, we introduced the maincontents in this paper finally.2. In section two, it was studied that a SEIRS epidemic model with an age-structured.Firstly, we described the model and carried on a simplification. Then, we used classiccharacteristic line method to give the equal integral calculus equation of the model andproved the existence and uniqueness of solution and the solution to the continuous depen-dence of initial-value. Finally we gave the locally stability of infection-free equilibrium.3. In section three, we studied with an age-structured and impulsive vaccinationSEIRS epidemic model. Firstly, we described the model and carried on a conversion,got its simplification form. Then we made transformation to the time of pulse, make itbecome the boundary and initial conditions. Made use of the result of continuous model,we got the existence and uniqueness of solution with an age-structured and impulsivevaccination SEIRS epidemic model.