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Dynamically consistent non-standard finite difference schemes for the MSEIR epidemiological model

Yves Dumont 1 Roumen Anguelov Jean M.-S Lubuma Meir Shillor
1 UMR AMAP - Botanique et Modélisation de l'Architecture des Plantes et des Végétations
Abstract : We construct a family of non-standard finite difference schemes that are dynamically consistent with the MSEIR model in the sense that they replicate the global asymptotic stability of the disease-free equilibrium, the local asymptotic stability of the endemic equilibrium, as well as the positivity of exact solutions and the conservation of the population of the continuous model.
Keywords : Dynamical systems asymptotic stability conservation of population positivity non-standard finite difference method
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http://hal.cirad.fr/cirad-00454770
Contributor : Yves Dumont <>
Submitted on : Tuesday, February 9, 2010 - 11:54:38 AM
Last modification on : Tuesday, March 17, 2020 - 3:14:15 AM

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  • HAL Id : cirad-00454770, version 1

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Yves Dumont, Roumen Anguelov, Jean M.-S Lubuma, Meir Shillor. Dynamically consistent non-standard finite difference schemes for the MSEIR epidemiological model. ICNAAM 2009, Sep 2009, Rethymno, Greece. pp.1213-1217. ⟨cirad-00454770⟩

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