Global analysis of an age-structured SEIR endemic model

In the present study, an age-structured SEIR endemic model is considered. The population is assumed to be not constant due to different inflows and outflows that are imbalanced by demographics, and migration etc. An abstract Cauchy problem is formulated from the model in order to show that the model is well-posed. The local and global stability of the disease-free steady state is examined using the basic reproduction number R0. Under certain condition, the endemic steady state is shown to be exist and locally stable. To illustrate the main theorems, sample simulations are presented at the end of the paper.