Age-structured models with nonlocal diffusion of dirichlet type. II: Global dynamics

Age-structured models with nonlocal diffusion arise naturally in describing the population dynamics of biological species and the transmission dynamics of infectious diseases in which individuals disperse nonlocally and interact each other, and the age structure of individuals matters. In the second part of this series of papers, we study the effects of principal eigenvalues on the global dynamics of the equation with monotone nonlinearity on the birth rate. More precisely, we analyze the existence and uniqueness of a nontrivial equilibrium and its stability for the age-structured model with nonlocal diffusion under certain assumptions via the sign of spectral bound of a linearized operator. Moreover, we investigate the asymptotic properties of the nontrivial equilibrium with respect to the diffusion rate and diffusion range.