A numerical method for the stability analysis of linear age-structured models with nonlocal diffusion
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We numerically investigate the stability of linear age-structured population models with nonlocal diffusion, which arise naturally in describing dynamics of infectious diseases. Compared to Laplace diffusion, the analysis of models with nonlocal diffusion is more challenging since the associated 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 associated to the semigroup. We propose 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 is provided in the case of separable model coefficients. Results are confirmed experimentally and numerical tests are presented also for the more general instance.
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