The aim of this paper is to design appropriate nonstandard finite difference (NSFD) schemes for two population mathematical models based on coupled nonlinear ordinary differential equations. Our work clarifies existing constructions of NSFD schemes for these two population models, which are not in full compliance with Mickens' methodology. We select the denominator functions for the discrete first-order derivatives depending on the existence of conservation laws, by following empirical rules suggested by Mickens. We fix nonlocal discretizations that preserve positivity of the schemes, irrespective of the value of the step size. Thus, our NSFD schemes are dynamically consistent with the two population models. We conduct a numerical study to assess the performance of the NSFD method.

本文的目的是为基于耦合非线性常微分方程的两个总体数学模型设计适当的非标准有限差分（NSFD）方案。我们的工作阐明了这两种人口模型的NSFD方案的现有结构，这与Mickens的方法不完全一致。通过遵循米肯斯（Mickens）提出的经验规则，我们根据守恒定律的存在为离散的一阶导数选择分母函数。我们修复了非局部离散化，该离散化保留了方案的积极性，而与步长的值无关。因此，我们的NSFD方案与两个总体模型动态一致。我们进行了一项数值研究，以评估NSFD方法的性能。