Dynamics Analysis Of Epidemic Model With Age-structured

In this paper we mainly study the age-structured epidemic model with theintervention. Assuming the isolation measures are taken and the patients haverecovery capability during the incubation, quarantine and infected period, we es-tablish a class of age-structured epidemic models. Secondly, we consider the infu-ence of drug therapy on the spread of the virus and a dynamic model of HIV withage-structured is established.The thesis is composed of three chapters:In the frst chapter, we mainly introduces the history of the development ofinfectious disease and progresses in this feld so far, as well as the signifcance ofstudying the infectious disease, and simply introduce the problems we study in thispaper.In the second chapter, we established the age-structured MSEIQR model withrecovery capability and infectious ability of the patient in latent period, isolationperiod, and infected period, and proved the existence and uniqueness of the endemicequilibrium, we also study the global dynamics of the disease-free equilibrium andthe endemic equilibrium, the sufcient conditions for the global stability of thedisease-free equilibrium and for the local stability of the infected equilibrium areobtained. We build the macroscopic epidemic model by dividing the populationinto several parts, and analysis the spread and development of diseases, that playa positive role in the prevention of infections diseases.In the third chapter, we studied a class of age-structured HIV model withHolling-â…¡infection rate, that takes into account the efects of both entry inhibitorsand protease inhibitors is considered, and the basic reproduction number expres-sion and the existence of equilibrium are obtained, we also proved that if R0>1,the infection equilibrium is only, and the infection-free equilibrium and the infec-tion equilibrium are studied by constructing two Lyapunov function respectively.Specifcally, when R0<1, the infection-free equilibrium E0is global asymptotical-ly stable; when R0>1, E0is unstable, and the infection equilibrium E is globalasymptotically stable. According to the interaction between the virus and immunecells, the microscopic dynamic model of infections disease are built to study thechanges of the system state with time changing, the dynamic behavior of the virusand the immune system can be efectively refect. Helping get the best treatment time.