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Mathematics > Numerical Analysis

arXiv:2304.10835 (math)
[Submitted on 21 Apr 2023 (v1), last revised 4 Sep 2023 (this version, v2)]

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

Authors:Dimitri Breda, Simone De Reggi, Rossana Vermiglio
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Abstract: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 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 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 coefficients. Results are confirmed experimentally and numerical tests are presented also for the more general instance.
Comments: 23 pages, 11 figures
Subjects: Numerical Analysis (math.NA); Dynamical Systems (math.DS)
MSC classes: 34L16, 47D99, 65L15, 65L60, 92D25
Cite as: arXiv:2304.10835 [math.NA]
  (or arXiv:2304.10835v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2304.10835
Journal reference: SIAM Journal on Scientific Computing, 46 (2), A953-A973, 2024
Related DOI: https://doi.org/10.1137/23M1568971

Submission history

From: Simone De Reggi [view email]
[v1] Fri, 21 Apr 2023 09:23:22 UTC (2,481 KB)
[v2] Mon, 4 Sep 2023 12:07:31 UTC (2,409 KB)
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