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

Anguelov R., Dumont Y., Lubuma J., Shillor M.. 2009. In : Psihoyios George (ed.), Tsitouras C. (ed.), Simos Theodore E. (ed.). Numerical analysis and applied mathematics : International Conference on Numerical Analysis and Applied Mathematics 2009, Rethymno, Crete, Greece, 18-22 September 2009. Melville : AIP, p. 1213-1216. (AIP Conference proceedings, 1168). International Conference on Numerical Analysis and Applied Mathematics 2009, 2009-09-18/2009-09-22, Rethymnon (Grèce).

DOI: 10.1063/1.3241286

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. (Résumé d'auteur)

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