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On nonstandard finite difference schemes in biosciences

We design, analyze and implement nonstandard finite difference (NSFD) schemes for some differential models in biosciences. The NSFD schemes are reliable in three directions. They are topologically dynamically consistent for onedimensional models. They can replicate the global asymptotic stability of...

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Detalles Bibliográficos
Autores principales: Anguelov, R., Dumont, Y., Lubuma, J. M.-S.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: American Institute of Physics 2012
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7108777/
https://www.ncbi.nlm.nih.gov/pubmed/32255872
http://dx.doi.org/10.1063/1.4758961
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author Anguelov, R.
Dumont, Y.
Lubuma, J. M.-S.
author_facet Anguelov, R.
Dumont, Y.
Lubuma, J. M.-S.
author_sort Anguelov, R.
collection PubMed
description We design, analyze and implement nonstandard finite difference (NSFD) schemes for some differential models in biosciences. The NSFD schemes are reliable in three directions. They are topologically dynamically consistent for onedimensional models. They can replicate the global asymptotic stability of the disease-free equilibrium of the MSEIR model in epidemiology whenever the basic reproduction number is less than 1. They preserve the positivity and boundedness property of solutions of advection-reaction and reaction-diffusion equations.
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spelling pubmed-71087772020-04-01 On nonstandard finite difference schemes in biosciences Anguelov, R. Dumont, Y. Lubuma, J. M.-S. AIP Conf Proc Article We design, analyze and implement nonstandard finite difference (NSFD) schemes for some differential models in biosciences. The NSFD schemes are reliable in three directions. They are topologically dynamically consistent for onedimensional models. They can replicate the global asymptotic stability of the disease-free equilibrium of the MSEIR model in epidemiology whenever the basic reproduction number is less than 1. They preserve the positivity and boundedness property of solutions of advection-reaction and reaction-diffusion equations. American Institute of Physics 2012-10-02 /pmc/articles/PMC7108777/ /pubmed/32255872 http://dx.doi.org/10.1063/1.4758961 Text en All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Anguelov, R.
Dumont, Y.
Lubuma, J. M.-S.
On nonstandard finite difference schemes in biosciences
title On nonstandard finite difference schemes in biosciences
title_full On nonstandard finite difference schemes in biosciences
title_fullStr On nonstandard finite difference schemes in biosciences
title_full_unstemmed On nonstandard finite difference schemes in biosciences
title_short On nonstandard finite difference schemes in biosciences
title_sort on nonstandard finite difference schemes in biosciences
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7108777/
https://www.ncbi.nlm.nih.gov/pubmed/32255872
http://dx.doi.org/10.1063/1.4758961
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