A numerical method for the stability analysis of linear age-structured models with nonlocal diffusion

We numerically address the stability analysis of linear age-structured population models with nonlocal diffusion, which arise naturally in describing dynamics of infectious diseases. Compared to Laplace diffusion, models with nonlocal diffusion are more challenging since the associ- ated semigroups have no regularizing properties in the spatial variable. Nevertheless, the asymptotic stability of the null equilibrium is determined by the spectrum of the infinitesimal generator asso- ciated to the semigroup. We propose a numerical method to approximate the leading part of this spectrum by first reformulating the problem via integration of the age-state and then by discretizing the generator combining a spectral projection in space with a pseudospectral collocation in age. A rigorous convergence analysis proving spectral accuracy is provided in the case of separable model coeffiients. Results are confirmed experimentally and numerical tests are presented also for the more general instance.