Analysis Of An SIR Infectious Disease With Age Structure

By establishing a reasonably and accurately epidemic model, people can effectivelyresearch and analyze the spread of infective diseases, and by detecting the propagation law,the spread of infective diseases can be effectively prevented and controlled. The subjecthas been causing wide concern.In 1927, Kenrmack and Mcendrick explored the rules of thespread of infective disease by using dynamics. So far, epidemic models mainly include inordernary di?erential model, partial differential model, mixed model and discrete model.In this paper, we establish and discuss a SIR epidemic model with age structure, andconsider that mortality because of disease is not zero. It is in accord with facts. Ourresearches provide the realistic basis for predicting and controlling the spread of someepidemic diseases.This paper includes four parts.In first part, we establish SIR epidemic model with age structure , and solve the solu-tion by using characteristic line method . It is easy to know the existence and uniquenessof solution.In second part, we obtain the expression of the basic reproduction number. It isproved that the disease become extinct if R₀ < 1 , and we give its biological significance.In third part, the persistence is discussed. We obtain that weak persistence andstrong persistence are hold if R₀ > 1 .In last part, we give a numerical simulation.