Analysis Of An Age-Structured Epidemic Model With Vertical Transmission

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 humansurvival and the national economy and people’s livelihood. Therefore, there is of greatimportance to study epidemic models. in this paper Analysis of An Age-Structured Epi-demic Model With Vertical Transmission which consists of the following two parts:In the second chapter, we discuss an age-structured SI epidemic model with vacci-nation and vertical transmission, and get the disease-free equilibrium. In addition, thereexists at least one endemic equilibrium if T₁>1. The disease-free equilibrium and en-demic equilibrium are both locally asymptotically stable if T₂<1, and both of them areunstable if T₂>1.In the third chapter, we discuss an age-structured SEI epidemic model with verticaltransmission, and obtain the disease-free equilibrium. In addition, there exists at leastone endemic equilibrium if R00>1. The disease-free equilibrium is locally asymptot-ically stable if R₀<1, and is unstable if R₀>1. The endemic equilibrium is locallyasymptotically stable if R₀₀>1and R₀<1.