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.
翻译：我们通过数值方法研究了非局部扩散时的线性年龄结构人口模型的稳定性，该模型自然地描述了传染病的动态。与拉普拉斯扩散相比，分析带有非局部扩散的模型更具挑战性，因为相关半群在空间变量中没有正则化属性。然而，零平衡点的渐进稳定性取决于与半群相关的无穷小生成器的频谱。我们建议通过首先通过年龄状态积分重构问题，然后将空间上的谱投影与年龄伪谱余项的联合离散化来逼近该频谱的主要部分。在可分离模型系数的情况下，我们提供了严格的收敛性分析。结果通过实验证实，并针对更一般的情况进行了数值测试。
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