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

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.