Recently, Hoang and Egbelowo (Boletin de la Sociedad Matemàtica Mexicana, 2020) proposed a nonstandard finite difference scheme (NSFD) to get a discrete SIR epidemic model with saturated incidence rate and constant vaccination. The discrete model was derived by discretizing the right-hand sides of the system locally and the first order derivative is approximated by the generalized forward difference method but with a restrictive denominator function. Their analysis showed that the NSFD scheme is dynamically-consistent only for relatively small time-step sizes. In this paper, we propose and analyze an alternative NSFD scheme by applying nonlocal approximation and choosing the denominator function such that the proposed scheme preserves the boundedness of solutions. It is verified that the proposed discrete model is dynamically-consistent with the corresponding continuous model for all time-step size. The analytical results have been confirmed by some numerical simulations. We also show numerically that the proposed NSFD scheme is superior to the Euler method and the NSFD method proposed by Hoang and Egbelowo (2020).

中文翻译：

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具有饱和发生率和接种率的SIR流行病模型的非标数值离散化。

最近，Hoang和Egbelowo（墨西哥《墨西哥邮编》，2020年）提出了一种非标准的有限差分方案（NSFD），以获得具有饱和发病率和恒定疫苗接种的离散SIR流行病模型。通过局部离散系统的右侧来导出离散模型，并通过广义前向差分法对一阶导数进行近似，但具有限制分母函数。他们的分析表明，NSFD方案仅在相对较小的时间步长下才具有动态一致性。在本文中，我们通过应用非局部逼近并选择分母函数，提出并分析了另一种NSFD方案，从而使该方案保留了解的有界性。验证了所提出的离散模型在所有时间步长上都与相应的连续模型动态一致。分析结果已通过一些数值模拟得到证实。我们还从数值上显示，提出的NSFD方案优于Hoang和Egbelowo（2020）提出的Euler方法和NSFD方法。