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：[abstract] 我们数值研究了具有非局部扩散的线性年龄结构种群模型的稳定性，此类模型自然产生于描述传染病的动力学中。与拉普拉斯扩散相比，非局部扩散模型的分析更具挑战性，因为相关半群在空间变量上缺乏正则化性质。尽管如此，零平衡态的渐近稳定性仍由半群对应的无穷小生成元的谱决定。我们提出通过先对年龄状态积分重构问题，再结合空间谱投影与年龄伪谱配点法离散生成元，来近似该谱的主导部分。在模型系数可分离情形下给出了严格的收敛性分析。数值实验验证了理论结果，同时针对更一般情形也给出了数值测试。