Analysis Of An Age-Structured Epidemic Model With Vaccination

The enemy of infectious diseases has always been harm to human health, The pop-ularity of infectious diseases in history again and again brought great disaster to human survival and social civilization. Therefore,there is of great importance to study epidemic models. In this paper,analysis of an age-structured SEI epidemic model with vaccination and vertical transmission which consists of the following two parts:In the first chapter, we discuss an age-structured SEI epidemic model with vac-cination and vertical transmission, and get the threshold and endemic equilibrium. In addition,it is proved that there exists only disease-free equilibrium if Rq<1, disease-free equilibrium and endemic equilibrium if R0>1.In the second chapter, we discuss another expression R0+of threshold in this model, and analysis the local asymptotic stable of this equilibrium. In addition, we obtain the endemic equilibrium is locally asymptotically stable if R0+>1; the disease-free equilibrium is locally asymptotically stable if R0+<1.