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A nonstandard numerical scheme of predictor–corrector type for epidemic models

✍ Scribed by Abraham J. Arenas; Gilberto González-Parra; Benito M. Chen-Charpentier

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
774 KB
Volume
59
Category
Article
ISSN
0898-1221

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✦ Synopsis

In this paper 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.

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