On nonstandard finite difference schemes in biosciences

Dumont Yves. 2012. On nonstandard finite difference schemes in biosciences. In : Application of Mathematics in Technical and Natural Sciences : Proccedings of the 4th International Conference - AMiTaNS'12, Varna, Bulgaria, June 11-16, 2012. eds. Todorov Michail D., Christov Christo I. Melville : AIP, 212-219. (AIP Conference Proceedings, 1487) ISBN 978-0-7354-1099-2 Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences. 4, Varna, Bulgarie, 11 Juin 2012/16 Juin 2012.

Résumé : 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.

Classification Agris : U10 - Informatique, mathématiques et statistiques
L73 - Maladies des animaux
H20 - Maladies des plantes

Auteurs et affiliations

• Dumont Yves, CIRAD-BIOS-UMR AMAP (FRA) ORCID: 0000-0003-4817-685X

Source : Cirad - Agritrop (https://agritrop.cirad.fr/566051/)

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