Dynamics Analysis Of An SIR Epidemic Model With Time Delay

This paper studied two kinds of infectious disease models, the one withdistributed time delay and the other one with vaccination strategy, the stability of themodels were studied respectively, and acquired some conclusions. The main results ofthe dissertation can be summarized as follows:The work background，the purpose and the valuable significance of infectiousdisease research,the current research situation in domestic and overseas,development historyof infectious diseases, were summarized in the first part of the paper, and in this partwe also introduced the main work of the paper.In chapter2, we discussed the stability of the infectious diseases model with timedelay. Firstly, we got the condition for the global stability of the disease-freeequilibrium in such system. Then the condition of stability of the system were studiedthrough the method in literature [2].In the third part, we had a research on the disease-free periodic solution of theinfectious disease models with pulse vaccination, and obtained its sufficient conditionof the globally attractivity of disease-free equilibrium point,then we showed thepermanent condition of the epidemic model,lastly we compared these two kinds ofvaccination.The fourth part of the paper had an summarize of this paper, and prospected thedirection of the later research and the future development of epidemiology.