[SS05] Data and model driven - study on infectious diseases modelling

[SS05-02] The Effects of Age Structure on Principal Eigenvalues of Reaction-Diffusion Equations

*Hao Kang¹ (1. Tianjin University (China))

Keywords:

Age structure,Diffusion operators,Principal eigenvalues,Monotonicity,Limiting behavior,Level sets

We study the role of age structure in determining the dynamics of reaction-diffusion equations. More precisely, by comparing principal eigenvalues between a diffusion operator with age structure and another one without age structure, we find that the former one is more complicated than the latter one and there even does not exist a determined relation between them in the limiting sense with respect to the diffusion rate. As an application, we will investigate the complicated behavior of basic reproduction number in diffusive epidemic models with age structure.