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新型冠状病毒肺炎传播的分数阶数学建模

Fractional order mathematical modeling of COVID-19 transmission.

作者信息

Ahmad Shabir, Ullah Aman, Al-Mdallal Qasem M, Khan Hasib, Shah Kamal, Khan Aziz

机构信息

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

Department of Mathematical Sciences, United Arab Emirates University, P.o Box 15551, Al Ain, Abu Dhabi, UAE.

出版信息

Chaos Solitons Fractals. 2020 Oct;139:110256. doi: 10.1016/j.chaos.2020.110256. Epub 2020 Sep 2.

DOI:10.1016/j.chaos.2020.110256
PMID:32905156
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7466947/
Abstract

In this article, the mathematical model with different compartments for the transmission dynamics of coronavirus-19 disease (COVID-19) is presented under the fractional-order derivative. Some results regarding the existence of at least one solution through fixed point results are derived. Then for the concerned approximate solution, the modified Euler method for fractional-order differential equations (FODEs) is utilized. Initially, we simulate the results by using some available data for different fractional-order to show the appropriateness of the proposed method. Further, we compare our results with some reported real data against confirmed infected and death cases per day for the initial 67 days in Wuhan city.

摘要

在本文中，提出了在分数阶导数下用于新型冠状病毒肺炎（COVID - 19）传播动力学的具有不同隔室的数学模型。通过不动点结果得出了关于至少存在一个解的一些结果。然后对于相关的近似解，使用了分数阶微分方程（FODEs）的改进欧拉方法。最初，我们通过使用不同分数阶的一些可用数据来模拟结果，以表明所提方法的适用性。此外，我们将我们的结果与一些报告的实际数据进行比较，这些数据是关于武汉市最初67天每天的确诊感染病例和死亡病例。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/d58e6cae309c/gr10_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/79127714d4b1/gr1_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/3189ee3617ae/gr2_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/47c842a51fde/gr3_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/968312e89bc5/gr4_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/2173f4abf5f2/gr5_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/97ede4db700c/gr6_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/9979837fa336/gr7_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/91e0927f2929/gr8_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/3cb555cfba3e/gr9_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/d58e6cae309c/gr10_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/79127714d4b1/gr1_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/3189ee3617ae/gr2_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/47c842a51fde/gr3_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/968312e89bc5/gr4_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/2173f4abf5f2/gr5_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/97ede4db700c/gr6_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/9979837fa336/gr7_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/91e0927f2929/gr8_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/3cb555cfba3e/gr9_lrg.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5771/7466947/d58e6cae309c/gr10_lrg.jpg

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