新冠病毒 compartmental 模型分析：一种数学与计算方法。

Analysis of a COVID-19 compartmental model: a mathematical and computational approach.

作者信息

Abreu Zita, Cantin Guillaume, Silva Cristiana J

机构信息

Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal.

Laboratoire de Mathématiques Appliquées, FR-CNRS-3335, 25, Rue Philippe Lebon, Le Havre Normandie 76063, France.

出版信息

Math Biosci Eng. 2021 Sep 14;18(6):7979-7998. doi: 10.3934/mbe.2021396.

DOI:10.3934/mbe.2021396

PMID:34814285

Abstract

In this note, we consider a compartmental epidemic mathematical model given by a system of differential equations. We provide a complete toolkit for performing both a symbolic and numerical analysis of the spreading of COVID-19. By using the free and open-source programming language Python and the mathematical software SageMath, we contribute for the reproducibility of the mathematical analysis of the stability of the equilibrium points of epidemic models and their fitting to real data. The mathematical tools and codes can be adapted to a wide range of mathematical epidemic models.

摘要

在本笔记中，我们考虑一个由微分方程组给出的分区流行数学模型。我们提供了一个完整的工具包，用于对新冠病毒（COVID-19）的传播进行符号分析和数值分析。通过使用免费的开源编程语言Python和数学软件SageMath，我们为流行病模型平衡点稳定性的数学分析及其对实际数据的拟合的可重复性做出了贡献。这些数学工具和代码可适用于广泛的数学流行病模型。