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中国武汉地区新冠肺炎疾病分数阶数学模型的数值模拟。

A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China.

作者信息

Yadav Ram Prasad

机构信息

Department of Mathematics, SRM University, Delhi-NCR Sonepat, Harayana, 131029, India.

Department of Mathematics, B. N. MANDAL University, Madhepura, Bihar, 852113, India.

出版信息

Chaos Solitons Fractals. 2020 Nov;140:110124. doi: 10.1016/j.chaos.2020.110124. Epub 2020 Jul 16.

Abstract

The novel Covid-19 was identified in Wuhan China in December, 2019 and has created medical emergency world wise and distorted many life in the couple of month, it is being burned challenging situation for the medical scientist and virologists. Fractional order derivative based modeling is quite important to understand the real world problems and to analyse realistic situation of the proposed model. In the present investigation a fractional model based on Caputo-Fabrizio fractional derivative has been developed for the transmission of CORONA VIRUS (COVID-19) in Wuhan China. The existence and uniqueness solutions of the fractional order derivative has been investigated with the help of fixed point theory. Adamas- Bashforth numerical scheme has been used in the numerical simulation of the Caputo-Fabrizio fractional order derivative. The analysis of susceptible population, exposed population, infected population, recovered population and concentration of the virus of COVID-19 in the surrounding environment with respect to time for different values of fractional order derivative has been shown by means of graph. The comparative analysis has also been performed from classical model and fractional model along with the certified experimental data.

摘要

新型冠状病毒肺炎于2019年12月在中国武汉被发现,在短短几个月内就引发了全球医疗紧急情况,并扰乱了许多人的生活,这给医学科学家和病毒学家带来了极具挑战性的局面。基于分数阶导数的建模对于理解现实世界问题以及分析所提出模型的实际情况非常重要。在本研究中,已开发出一种基于卡普托 - 法布里齐奥分数阶导数的分数模型,用于中国武汉新冠病毒(COVID - 19)的传播。借助不动点理论研究了分数阶导数的存在性和唯一性解。亚当斯 - 巴什福斯数值格式已用于卡普托 - 法布里齐奥分数阶导数的数值模拟。通过图形展示了对于不同分数阶导数值,易感人群、暴露人群、感染人群、康复人群以及周围环境中新冠病毒浓度随时间的分析情况。还对经典模型和分数模型与经认证的实验数据进行了对比分析。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/0eb5/7365131/7d3e54470b5c/gr1_lrg.jpg

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