A numerical method for the stability analysis of linear age-structured models with nonlocal diffusion
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910363166965760 |
|---|---|
| author | Breda, Dimitri De Reggi, Simone Vermiglio, Rossana |
| author_facet | Breda, Dimitri De Reggi, Simone Vermiglio, Rossana |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_10835 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A numerical method for the stability analysis of linear age-structured models with nonlocal diffusion Breda, Dimitri De Reggi, Simone Vermiglio, Rossana Numerical Analysis Dynamical Systems 34L16, 47D99, 65L15, 65L60, 92D25 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. |
| title | A numerical method for the stability analysis of linear age-structured models with nonlocal diffusion |
| topic | Numerical Analysis Dynamical Systems 34L16, 47D99, 65L15, 65L60, 92D25 |
| url | https://arxiv.org/abs/2304.10835 |