Spatio-temporal behaviour of SIR models with cross-diffusion and vital dynamics
Contemporary epidemiological models often involve spatial variation, providing an avenue to investigate the averaged dynamics of individual movements. In this work, we extend a recent model by Vaziry, Kolokolnikov, and Kevrekidis [Royal Society Open Science 9 (10), 2022] that included, in both infec...
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Cambridge University Press
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| Series: | European Journal of Applied Mathematics |
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| author | Maryam Ahmadpoortorkamani Alexei Cheviakov |
| author_facet | Maryam Ahmadpoortorkamani Alexei Cheviakov |
| author_sort | Maryam Ahmadpoortorkamani |
| collection | DOAJ |
| description | Contemporary epidemiological models often involve spatial variation, providing an avenue to investigate the averaged dynamics of individual movements. In this work, we extend a recent model by Vaziry, Kolokolnikov, and Kevrekidis [Royal Society Open Science 9 (10), 2022] that included, in both infected and susceptible population dynamics equations, a cross-diffusion term with the second spatial derivative of the infected population density. Diffusion terms of this type occur, for example, in the Keller–Siegel chemotaxis model. The presented model corresponds to local orderly commute of susceptible and infected individuals and is shown to arise in two dimensions as a limit of a discrete process. The present contribution identifies and studies specific features of the new model’s dynamics, including various types of infection waves and buffer zones protected from the infection. The model with vital dynamics additionally exhibits complex spatio-temporal behaviour that involves the generation of quasiperiodic infection waves and emergence of transient strongly heterogeneous patterns. |
| format | Article |
| id | doaj-art-67fad018788641a5aa87bc4f1b668c3d |
| institution | Kabale University |
| issn | 0956-7925 1469-4425 |
| language | English |
| publisher | Cambridge University Press |
| record_format | Article |
| series | European Journal of Applied Mathematics |
| spelling | doaj-art-67fad018788641a5aa87bc4f1b668c3d2025-01-16T21:51:09ZengCambridge University PressEuropean Journal of Applied Mathematics0956-79251469-442512110.1017/S095679252400086XSpatio-temporal behaviour of SIR models with cross-diffusion and vital dynamicsMaryam Ahmadpoortorkamani0Alexei Cheviakov1https://orcid.org/0000-0002-9647-3683Department of Mathematics and Statistics, University of Saskatchewan, CanadaDepartment of Mathematics and Statistics, University of Saskatchewan, CanadaContemporary epidemiological models often involve spatial variation, providing an avenue to investigate the averaged dynamics of individual movements. In this work, we extend a recent model by Vaziry, Kolokolnikov, and Kevrekidis [Royal Society Open Science 9 (10), 2022] that included, in both infected and susceptible population dynamics equations, a cross-diffusion term with the second spatial derivative of the infected population density. Diffusion terms of this type occur, for example, in the Keller–Siegel chemotaxis model. The presented model corresponds to local orderly commute of susceptible and infected individuals and is shown to arise in two dimensions as a limit of a discrete process. The present contribution identifies and studies specific features of the new model’s dynamics, including various types of infection waves and buffer zones protected from the infection. The model with vital dynamics additionally exhibits complex spatio-temporal behaviour that involves the generation of quasiperiodic infection waves and emergence of transient strongly heterogeneous patterns.https://www.cambridge.org/core/product/identifier/S095679252400086X/type/journal_articlePDE SIR modelcross-diffusionexact solutions35Q9235G2035B06 |
| spellingShingle | Maryam Ahmadpoortorkamani Alexei Cheviakov Spatio-temporal behaviour of SIR models with cross-diffusion and vital dynamics European Journal of Applied Mathematics PDE SIR model cross-diffusion exact solutions 35Q92 35G20 35B06 |
| title | Spatio-temporal behaviour of SIR models with cross-diffusion and vital dynamics |
| title_full | Spatio-temporal behaviour of SIR models with cross-diffusion and vital dynamics |
| title_fullStr | Spatio-temporal behaviour of SIR models with cross-diffusion and vital dynamics |
| title_full_unstemmed | Spatio-temporal behaviour of SIR models with cross-diffusion and vital dynamics |
| title_short | Spatio-temporal behaviour of SIR models with cross-diffusion and vital dynamics |
| title_sort | spatio temporal behaviour of sir models with cross diffusion and vital dynamics |
| topic | PDE SIR model cross-diffusion exact solutions 35Q92 35G20 35B06 |
| url | https://www.cambridge.org/core/product/identifier/S095679252400086X/type/journal_article |
| work_keys_str_mv | AT maryamahmadpoortorkamani spatiotemporalbehaviourofsirmodelswithcrossdiffusionandvitaldynamics AT alexeicheviakov spatiotemporalbehaviourofsirmodelswithcrossdiffusionandvitaldynamics |