Qualitatively Correct Numerical Methods for the Basic Ross–Macdonald Malaria Model

Faragó, István and Mincsovics, Miklós Emil and Mosleh, Rahele (2022) Qualitatively Correct Numerical Methods for the Basic Ross–Macdonald Malaria Model. In: Progress in Industrial Mathematics at ECMI 2021. Mathematics in industry (39). Springer International Publishing, Cham, pp. 75-81. ISBN 9783031118173; 9783031118180

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Abstract

We investigate the qualitative performance of different numerical methods applied to the Ross-Macdonald malaria model. It is known that for this model a certain set is positively invariant and the question is that the discrete system which is obtained from the model by the application of a numerical method possesses this property or not. This property called dynamical consistency is the objective of this study. We consider a method qualitatively correct if the resulted discrete system inherits this property. We investigate the explicit and implicit Euler methods, the latter also with Newton iteration as a sub-procedure, moreover a non-local discretization method and finally, the explicit Euler method combined with step-size functions.

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