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Comparison of some standard and nonstandard numerical methods 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. 1209-1212. (AIP Conference proceedings, 1168). International Conference on Numerical Analysis and Applied Mathematics 2009, 2009-09-18/2009-09-22, Rethymnon (Grèce).

DOI: 10.1063/1.3241285

The paper presents some non-standard finite difference methods for the MSEIR model. Following a short description of the methods, they are compared with the standard methods usually implemented in scientific software. It is shown that the non-standard schemes are superior to the standard ones with respect to their qualitative properties and the CPU running time. We show that non-local approximations of non linear terms in the equations can be of utmost importance to capture the dynamic of the system (Résumé d'auteur)

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