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Zbl 1198.65116
Arenas, Abraham J.; González-Parra, Gilberto; Chen-Charpentier, Benito M.
A nonstandard numerical scheme of predictor-corrector type for epidemic models. (English)
[J] Comput. Math. Appl. 59, No. 12, 3740-3749 (2010). ISSN 0898-1221

Summary: We construct and develop a competitive nonstandard finite difference numerical scheme of predictor-corrector type for the classical SIR epidemic model. This proposed scheme is designed with the aim of obtaining dynamical consistency between the discrete solution and the solution of the continuous model. The nonstandard finite difference scheme with Conservation Law (NSFDCL) developed here satisfies some important properties associated with the considered SIR epidemic model, such as positivity, boundedness, monotonicity, stability and conservation of frequency of the oscillations. Numerical comparisons between the NSFDCL numerical scheme developed here and Runge-Kutta type schemes show its effectiveness.

MSC 2000:: *65L06 Multistep, Runge-Kutta, and extrapolation methods
92D30 Epidemiology

Keywords: nonstandard finite difference schemes; numerical solution; epidemic model SIR; predictor-corrector

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