Principal spectral theory in multigroup age-structured models with nonlocal diffusion

In modeling the population dynamics of biological species and the transmission dynamics of infectious diseases, age-structure and nonlocal diffusion are two important components since individuals need to be mature enough to move and they disperse and interact each other nonlocally. In this paper we study the principal spectral theory of age-structured models with nonlocal diffusion within a population of multigroups. First, we provide a criterion on the existence of the principal eigenvalue by using the theory of positive resolvent operators with their perturbations. Then we define the generalized principal eigenvalue and use it to investigate the influence of diffusion rate on the principal eigenvalue. Next we establish the strong maximum principle for age-structured nonlocal diffusion operators. Finally, as an example we apply our established theory to an age-structured cooperative system with nonlocal diffusion.