离散时间 SIR 模型的精确解

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED Applied Numerical Mathematics Pub Date : 2024-09-12 DOI:10.1016/j.apnum.2024.09.014

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引用次数: 0

摘要

我们针对易感-感染-清除（SIR）连续模型提出了一种非标准有限差分方案。我们证明了离散化系统与其连续对应系统在动态上是一致的，并推导出其精确解。最后，我们分析了易感个体、受感染个体和被移除个体的长期行为，并举例说明了我们的结果。与现有文献中的 SIR 离散时模型相比，我们的新模型在数学和生物学上都是合理的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Exact solution for a discrete-time SIR model

We propose a nonstandard finite difference scheme for the Susceptible–Infected–Removed (SIR) continuous model. We prove that our discretized system is dynamically consistent with its continuous counterpart and we derive its exact solution. We end with the analysis of the long-term behavior of susceptible, infected and removed individuals, illustrating our results with examples. In contrast with the SIR discrete-time model available in the literature, our new model is simultaneously mathematically and biologically sound.

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.