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综合分析考虑环境和社交隔离因素的 COVID-19 非线性数学模型。

A comprehensive analysis of COVID-19 nonlinear mathematical model by incorporating the environment and social distancing.

机构信息

Department of Mathematics, University of Malakand, Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan.

Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586, Riyadh, Saudi Arabia.

出版信息

Sci Rep. 2024 May 28;14(1):12238. doi: 10.1038/s41598-024-61730-y.

DOI:10.1038/s41598-024-61730-y
PMID:38806539
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11133490/
Abstract

This research conducts a detailed analysis of a nonlinear mathematical model representing COVID-19, incorporating both environmental factors and social distancing measures. It thoroughly analyzes the model's equilibrium points, computes the basic reproductive rate, and evaluates the stability of the model at disease-free and endemic equilibrium states, both locally and globally. Additionally, sensitivity analysis is carried out. The study develops a sophisticated stability theory, primarily focusing on the characteristics of the Volterra-Lyapunov (V-L) matrices method. To understand the dynamic behavior of COVID-19, numerical simulations are essential. For this purpose, the study employs a robust numerical technique known as the non-standard finite difference (NSFD) method, introduced by Mickens. Various results are visually presented through graphical representations across different parameter values to illustrate the impact of environmental factors and social distancing measures.

摘要

本研究对一个包含环境因素和社交距离措施的 COVID-19 的非线性数学模型进行了详细分析。它彻底分析了模型的平衡点，计算了基本繁殖率，并评估了疾病无和地方病平衡点的模型稳定性，包括局部和全局的稳定性。此外，还进行了敏感性分析。该研究建立了一种复杂的稳定性理论，主要侧重于 Volterra-Lyapunov（V-L）矩阵方法的特性。为了了解 COVID-19 的动态行为，数值模拟是必不可少的。为此，本研究采用了一种称为 Mickens 提出的非标准有限差分（NSFD）方法的强大数值技术。通过不同参数值的图形表示来呈现各种结果，以说明环境因素和社交距离措施的影响。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/003302cad03d/41598_2024_61730_Fig15_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/0b0f5ed7c52b/41598_2024_61730_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/826c88812ffa/41598_2024_61730_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/57c9732654e7/41598_2024_61730_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/f897f12eadba/41598_2024_61730_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/7fe06b7fe742/41598_2024_61730_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/54ed13aea92d/41598_2024_61730_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/47342f042293/41598_2024_61730_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/7679be145fce/41598_2024_61730_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/c63079a83a01/41598_2024_61730_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/6f6bc58cdcfc/41598_2024_61730_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/0a497daa4c7f/41598_2024_61730_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/443b5674e84a/41598_2024_61730_Fig12_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/28b9890ca845/41598_2024_61730_Fig13_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/376c79480314/41598_2024_61730_Fig14_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/003302cad03d/41598_2024_61730_Fig15_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/0b0f5ed7c52b/41598_2024_61730_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/826c88812ffa/41598_2024_61730_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/57c9732654e7/41598_2024_61730_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/f897f12eadba/41598_2024_61730_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/7fe06b7fe742/41598_2024_61730_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/54ed13aea92d/41598_2024_61730_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/47342f042293/41598_2024_61730_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/7679be145fce/41598_2024_61730_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/c63079a83a01/41598_2024_61730_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/6f6bc58cdcfc/41598_2024_61730_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/0a497daa4c7f/41598_2024_61730_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/443b5674e84a/41598_2024_61730_Fig12_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/28b9890ca845/41598_2024_61730_Fig13_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/376c79480314/41598_2024_61730_Fig14_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/059c/11133490/003302cad03d/41598_2024_61730_Fig15_HTML.jpg

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