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基于有限差分法和无网格法的非线性COVID-19大流行模型的数值研究

Numerical study of a nonlinear COVID-19 pandemic model by finite difference and meshless methods.

作者信息

Zarin Rahat

机构信息

Department of Basic Sciences, University of Engineering and Technology, Peshawar, Khyber Pakhtunkhwa, Pakistan.

出版信息

Partial Differ Equ Appl Math. 2022 Dec;6:100460. doi: 10.1016/j.padiff.2022.100460. Epub 2022 Nov 4.

DOI:10.1016/j.padiff.2022.100460
PMID:36348759
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9633111/
Abstract

In this paper, a mathematical epidemiological model in the form of reaction diffusion is proposed for the transmission of the novel coronavirus (COVID-19). The next-generation method is utilized for calculating the threshold number R while the least square curve fitting approach is used for estimating the parameter values. The mathematical epidemiological model without and with diffusion is simulated through the operator splitting approach based on finite difference and meshless methods. Further, for the graphical solution of the non-linear model, we have applied a one-step explicit meshless procedure. We study the numerical simulation of the proposed model under the effects of diffusion. The stability analysis of the endemic equilibrium point is investigated. The obtained numerical results are compared mutually since the exact solutions are not available.

摘要

本文针对新型冠状病毒（COVID-19）的传播，提出了一种反应扩散形式的数学流行病学模型。利用下一代方法计算阈值数(R)，同时采用最小二乘曲线拟合方法估计参数值。基于有限差分和无网格方法的算子分裂方法，对有无扩散的数学流行病学模型进行了模拟。此外，对于非线性模型的图形解，我们应用了一步显式无网格程序。我们研究了所提出模型在扩散影响下的数值模拟。研究了地方病平衡点的稳定性分析。由于没有精确解，因此对得到的数值结果进行了相互比较。

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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b454/9633111/a55130241bf3/gr1_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b454/9633111/f9e2f23e582c/gr2_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b454/9633111/1f81b68a9aaf/gr3_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b454/9633111/7d76d0891a14/gr4_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b454/9633111/c0bf122b4f5b/gr5_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b454/9633111/5e1b305330e9/gr6_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b454/9633111/c0bf122b4f5b/gr7_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b454/9633111/48cb83f1d5cb/gr8_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b454/9633111/b37f6cf21ca9/gr9_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b454/9633111/15e9c8515c88/gr10_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b454/9633111/14be30d1467c/gr11_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b454/9633111/5f31251edc67/gr12_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/b454/9633111/b76cabf56f98/gr13_lrg.jpg

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