Global behavior of a multi-group SEIR epidemic model with age structure and spatial diffusion.

Different epidemic models with one or two characteristics of multi-group, age structure and spatial diffusion have been proposed, but few models take all three into consideration. In this paper, a novel multi-group SEIR epidemic model with both age structure and spatial diffusion is constructed for the first time ever to study the transmission dynamics of infectious diseases. We first analytically study the positivity, boundedness, existence and uniqueness of solution and the existence of compact global attractor of the associated solution semiflow. Based on some assumptions for parameters, we then show that the disease-free steady state is globally asymptotically stable by utilizing appropriate Lyapunov functionals and the LaSalle's invariance principle. By means of Perron-Frobenius theorem and graph-theoretical results, the existence and global stability of endemic steady state are ensured under appropriate conditions. Finally, feasibility of main theoretical results is showed with the aid of numerical examples for model with two groups which is important from the viewpoint of applications.