SARS-COV-2 的确定性数学模型的分析与比较研究：案例研究。

Analysis and comparative study of a deterministic mathematical model of SARS-COV-2 with fractal-fractional operators: a case study.

机构信息

Department of Mathematics, Government College University, Faisalabad, Punjab, 38040, Pakistan.

Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University(IMSIU), Riyadh, Saudi Arabia.

出版信息

Sci Rep. 2024 Mar 18;14(1):6431. doi: 10.1038/s41598-024-56557-6.

DOI:10.1038/s41598-024-56557-6

PMID:38499671

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11335959/

Abstract

In this paper, we investigate a fractal-fractional-order mathematical model with the influence of hospitalized patients and the impact of vaccination with fractal-fractional operators. The respective derivatives are considered in the Caputo, Caputo Fabrizio, and Atangana-Baleanu senses of fractional order and fractal dimension . For the proposed problem, some results regarding basic reproduction number and stability are given. Using the next-generation matrix approach, we have investigated the global and local stability of several types of equilibrium points. We provide a detailed analysis of the existence and uniqueness of the solution. Moreover, we fit the model with the real data of Pakistan from June 01, 2020, till March 24, 2021. Then, we use the fractal-fractional derivative to find a numerical solution for the model. MATLAB software is used for numerical illustration. Graphical presentations corresponding to different parameteric values are given as well.

摘要

在本文中，我们研究了一个带有住院患者影响和分形分数阶算子接种影响的分形分数阶数学模型。分别在 Caputo、Caputo Fabrizio 和 Atangana-Baleanu 意义下考虑分数阶导数和分形维数。针对所提出的问题，给出了一些关于基本再生数和稳定性的结果。我们使用下一代矩阵方法研究了几种平衡点的全局和局部稳定性。我们对解的存在性和唯一性进行了详细分析。此外，我们还使用 2020 年 6 月 1 日至 2021 年 3 月 24 日巴基斯坦的实际数据对模型进行拟合。然后，我们使用分形分数阶导数来为模型找到数值解。使用 MATLAB 软件进行数值说明。还给出了对应于不同参数值的图形表示。