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一种具有分数阶导数的新型新冠病毒数学模型。稳定性与数值分析。

A novel mathematics model of covid-19 with fractional derivative. Stability and numerical analysis.

作者信息

Alkahtani Badr Saad T, Alzaid Sara Salem

机构信息

Department of Mathematics, College of Science, King Saud University, P.O. Box 1142, Riyadh 11989, Saudi Arabia.

出版信息

Chaos Solitons Fractals. 2020 Sep;138:110006. doi: 10.1016/j.chaos.2020.110006. Epub 2020 Jun 17.

Abstract

a mathematical model depicting the spread of covid-19 epidemic and implementation of population covid-19 intervention in Italy. The model has 8 components leading to system of 8 ordinary differential equations. In this paper, we investigate the model using the concept of fractional differential operator. A numerical method based on the Lagrange polynomial was used to solve the system equations depicting the spread of COVID-19. A detailed investigation of stability including reproductive number using the next generation matrix, and the Lyapunov were presented in detail. Numerical simulations are depicted for various fractional orders.

摘要

一个描述意大利新冠疫情传播及人群新冠疫情干预措施实施情况的数学模型。该模型有8个组成部分,可导出一个由8个常微分方程组成的系统。在本文中,我们使用分数阶微分算子的概念对该模型进行研究。采用基于拉格朗日多项式的数值方法来求解描述新冠疫情传播的方程组。详细介绍了使用下一代矩阵和李雅普诺夫方法对包括再生数在内的稳定性进行的详细研究。给出了不同分数阶的数值模拟结果。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/d53c/7298553/8b582417aea0/gr1_lrg.jpg

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