新型冠状病毒（COVID-19）的数学建模与防控
Mathematical modeling for novel coronavirus (COVID-19) and control.
作者信息
Alqarni Marei Saeed, Alghamdi Metib, Muhammad Taseer, Alshomrani Ali Saleh, Khan Muhammad Altaf
机构信息
Department of Mathematics, College of Sciences King Khalid University Abha Saudi Arabia.
Department of Mathematics, Faculty of Science King Abdulaziz University Jeddah Saudi Arabia.
出版信息
Numer Methods Partial Differ Equ. 2022 Jul;38(4):760-776. doi: 10.1002/num.22695. Epub 2020 Nov 26.
Abstract
In the present investigations, we construct a new mathematical for the transmission dynamics of corona virus (COVID-19) using the cases reported in Kingdom of Saudi Arabia for March 02 till July 31, 2020. We investigate the parameters values of the model using the least square curve fitting and the basic reproduction number is suggested for the given data is ℛ ≈ 1.2937. The stability results of the model are shown when the basic reproduction number is ℛ < 1. The model is locally asymptotically stable when ℛ < 1. Further, we show some important parameters that are more sensitive to the basic reproduction number ℛ using the PRCC method. The sensitive parameters that act as a control parameters that can reduce and control the infection in the population are shown graphically. The suggested control parameters can reduce dramatically the infection in the Kingdom of Saudi Arabia if the proper attention is paid to the suggested controls.
摘要
在目前的研究中，我们利用沙特阿拉伯王国2020年3月2日至7月31日报告的病例，构建了一个关于冠状病毒（COVID-19）传播动力学的新数学模型。我们使用最小二乘曲线拟合来研究该模型的参数值，对于给定数据，建议的基本再生数为ℛ ≈ 1.2937。当基本再生数ℛ < 1时，展示了该模型的稳定性结果。当ℛ < 1时，模型是局部渐近稳定的。此外，我们使用PRCC方法展示了一些对基本再生数ℛ更敏感的重要参数。作为控制参数的敏感参数可以减少和控制人群中的感染，这些参数以图形方式展示。如果对建议的控制措施给予适当关注，建议的控制参数可以大幅减少沙特阿拉伯王国的感染情况。
相似文献
1
Mathematical modeling for novel coronavirus (COVID-19) and control.新型冠状病毒（COVID-19）的数学建模与防控
Numer Methods Partial Differ Equ. 2022 Jul;38(4):760-776. doi: 10.1002/num.22695. Epub 2020 Nov 26.
2
Mathematical modeling and analysis of COVID-19: A study of new variant Omicron.新型冠状病毒肺炎（COVID-19）的数学建模与分析：对新变种奥密克戎的研究
Physica A. 2022 Aug 1;599:127452. doi: 10.1016/j.physa.2022.127452. Epub 2022 Apr 26.
3
Modeling the impact of non-pharmaceutical interventions on the dynamics of novel coronavirus with optimal control analysis with a case study.通过案例研究，运用最优控制分析对非药物干预措施对新型冠状病毒动态的影响进行建模。
Chaos Solitons Fractals. 2020 Oct;139:110075. doi: 10.1016/j.chaos.2020.110075. Epub 2020 Jul 3.
4
Dynamics of fractional order COVID-19 model with a case study of Saudi Arabia.具有沙特阿拉伯案例研究的分数阶COVID-19模型动力学
Results Phys. 2021 Feb;21:103787. doi: 10.1016/j.rinp.2020.103787. Epub 2021 Jan 2.
5
A dynamical study of SARS-COV-2: A study of third wave.新型冠状病毒肺炎的动力学研究：第三波疫情研究
Results Phys. 2021 Oct;29:104705. doi: 10.1016/j.rinp.2021.104705. Epub 2021 Aug 22.
6
A new dynamical modeling SEIR with global analysis applied to the real data of spreading COVID-19 in Saudi Arabia.一种新的动力学 SEIR 模型与全球分析应用于沙特阿拉伯 COVID-19 传播的真实数据。
Math Biosci Eng. 2020 Oct 16;17(6):7018-7044. doi: 10.3934/mbe.2020362.
7
A Mathematical Model of Vaccinations Using New Fractional Order Derivative.一种使用新型分数阶导数的疫苗接种数学模型。
Vaccines (Basel). 2022 Nov 22;10(12):1980. doi: 10.3390/vaccines10121980.
8
A mathematical model of Coronavirus Disease (COVID-19) containing asymptomatic and symptomatic classes.一种包含无症状和有症状类别的冠状病毒病（COVID-19）数学模型。
Results Phys. 2021 Feb;21:103776. doi: 10.1016/j.rinp.2020.103776. Epub 2021 Jan 6.
9
Modeling and simulation of the novel coronavirus in Caputo derivative.新型冠状病毒在卡普托导数中的建模与仿真
Results Phys. 2020 Dec;19:103588. doi: 10.1016/j.rinp.2020.103588. Epub 2020 Nov 17.
10
Application of piecewise fractional differential equation to COVID-19 infection dynamics.分段分数阶微分方程在新型冠状病毒肺炎感染动力学中的应用
Results Phys. 2022 Aug;39:105685. doi: 10.1016/j.rinp.2022.105685. Epub 2022 Jun 4.
引用本文的文献
1
Fractional epidemic model of coronavirus disease with vaccination and crowding effects.带接种和拥挤效应的冠状病毒病分数阶模型。
Sci Rep. 2024 Apr 8;14(1):8157. doi: 10.1038/s41598-024-58192-7.
2
Cost-effectiveness analysis of COVID-19 intervention policies using a mathematical model: an optimal control approach.使用数学模型对 COVID-19 干预政策进行成本效益分析：最优控制方法。
Sci Rep. 2024 Jan 4;14(1):494. doi: 10.1038/s41598-023-50799-6.
3
Incidence rate drive the multiple wave in the COVID-19 pandemic.发病率推动了新冠疫情中的多波疫情。
MethodsX. 2023 Aug 6;11:102317. doi: 10.1016/j.mex.2023.102317. eCollection 2023 Dec.
4
Modelling COVID-19 pandemic control strategies in metropolitan and rural health districts in New South Wales, Australia.在澳大利亚新南威尔士州的城市和农村卫生区对 COVID-19 大流行控制策略进行建模。
Sci Rep. 2023 Jun 26;13(1):10352. doi: 10.1038/s41598-023-37240-8.
5
A Mathematical Model of Vaccinations Using New Fractional Order Derivative.一种使用新型分数阶导数的疫苗接种数学模型。
Vaccines (Basel). 2022 Nov 22;10(12):1980. doi: 10.3390/vaccines10121980.
6
Dynamical Analysis of COVID-19 Model Incorporating Environmental Factors.纳入环境因素的新冠肺炎模型动力学分析
Iran J Sci Technol Trans A Sci. 2022;46(6):1651-1666. doi: 10.1007/s40995-022-01372-9. Epub 2022 Nov 28.
7
Qualitative analysis of a fractional-order two-strain epidemic model with vaccination and general non-monotonic incidence rate.具有疫苗接种和一般非单调发病率的分数阶两菌株流行病模型的定性分析
Int J Dyn Control. 2022 Nov 22:1-12. doi: 10.1007/s40435-022-01083-4.
8
Numerical study of a nonlinear COVID-19 pandemic model by finite difference and meshless methods.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
Partial Differ Equ Appl Math. 2022 Dec;6:100460. doi: 10.1016/j.padiff.2022.100460. Epub 2022 Nov 4.
9
Optimal control and cost-effectiveness analysis of a new COVID-19 model for Omicron strain.针对奥密克戎毒株的新型新冠病毒模型的最优控制与成本效益分析
Physica A. 2022 Nov 15;606:128134. doi: 10.1016/j.physa.2022.128134. Epub 2022 Aug 25.
10
COVID-19 in Saudi Arabia: An Overview.沙特阿拉伯的 COVID-19：概述。
Front Public Health. 2022 Feb 2;9:736942. doi: 10.3389/fpubh.2021.736942. eCollection 2021.
本文引用的文献
1
Modeling and prediction of COVID-19 in Mexico applying mathematical and computational models.运用数学和计算模型对墨西哥的新冠疫情进行建模与预测。
Chaos Solitons Fractals. 2020 Sep;138:109946. doi: 10.1016/j.chaos.2020.109946. Epub 2020 May 29.
2
The dynamics of COVID-19 with quarantined and isolation.新冠病毒病在隔离和检疫情况下的动态变化
Adv Differ Equ. 2020;2020(1):425. doi: 10.1186/s13662-020-02882-9. Epub 2020 Aug 14.
3
Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana.考虑环境影响的新冠病毒全球稳定性及成本效益分析：以加纳数据为例
Chaos Solitons Fractals. 2020 Nov;140:110103. doi: 10.1016/j.chaos.2020.110103. Epub 2020 Jul 10.
4
Modeling the impact of non-pharmaceutical interventions on the dynamics of novel coronavirus with optimal control analysis with a case study.通过案例研究，运用最优控制分析对非药物干预措施对新型冠状病毒动态的影响进行建模。
Chaos Solitons Fractals. 2020 Oct;139:110075. doi: 10.1016/j.chaos.2020.110075. Epub 2020 Jul 3.
5
A novel covid-19 mathematical model with fractional derivatives: Singular and nonsingular kernels.一种具有分数阶导数的新型新冠病毒19数学模型：奇异核与非奇异核
Chaos Solitons Fractals. 2020 Oct;139:110060. doi: 10.1016/j.chaos.2020.110060. Epub 2020 Jun 28.
6
Analysis of a mathematical model for COVID-19 population dynamics in Lagos, Nigeria.尼日利亚拉各斯新冠病毒病（COVID-19）人群动态数学模型分析
Chaos Solitons Fractals. 2020 Oct;139:110032. doi: 10.1016/j.chaos.2020.110032. Epub 2020 Jun 20.
7
Forecasting the cumulative number of confirmed cases of COVID-19 in Italy, UK and USA using fractional nonlinear grey Bernoulli model.使用分数阶非线性灰色伯努利模型预测意大利、英国和美国新冠病毒病确诊病例的累计数量。
Chaos Solitons Fractals. 2020 Sep;138:109948. doi: 10.1016/j.chaos.2020.109948. Epub 2020 May 29.
8
Quantifying the role of social distancing, personal protection and case detection in mitigating COVID-19 outbreak in Ontario, Canada.量化社交距离、个人防护和病例检测在减轻加拿大安大略省新冠疫情中的作用。
J Math Ind. 2020;10(1):15. doi: 10.1186/s13362-020-00083-3. Epub 2020 May 26.
9
Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?用新的分形分数算子对COVID-19传播进行建模：封锁措施能否在疫苗接种前拯救人类？
Chaos Solitons Fractals. 2020 Jul;136:109860. doi: 10.1016/j.chaos.2020.109860. Epub 2020 May 29.
10
Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel Coronavirus.数学评估非药物干预措施对遏制 2019 年新型冠状病毒的影响。
Math Biosci. 2020 Jul;325:108364. doi: 10.1016/j.mbs.2020.108364. Epub 2020 May 1.
Zotero 插件