基于分数阶SIR模型的新冠肺炎疾病的传播预测
Prediction of Novel Coronavirus Pneumonia Transmission Based on Fractional SIR Model
DOI: 10.12677/AAM.2021.1010338, PDF,  被引量    科研立项经费支持
作者: 任 磊*, 米冬茜：商丘师范学院数学与统计学院，河南 商丘
关键词: 分数阶系统；新冠肺炎；SIR模型；Fractional System； COVID-19； SIR Model
摘要: 本文提出了用于预测新冠肺炎疾病传播的分数阶SIR (susceptible-infected-recovered)模型，基于Caputo分数阶导数的有限差分方法完成了时域模型的实现，然后研究了分数阶导数值对所提出的分数阶SIR模型的动态特性的影响。
Abstract: A novel coronavirus pneumonia model is proposed to predict the spread of new crown pneumonia disease. The SIR model (susceptible-infected-recovered) is implemented. The time domain model is implemented by the Caputo finite difference method with fractional derivative. Then the influence of fractional values on the dynamic characteristics of the fractional SIR model is studied.
文章引用：任磊, 米冬茜. 基于分数阶SIR模型的新冠肺炎疾病的传播预测[J]. 应用数学进展, 2021, 10(10): 3233-3238. https://doi.org/10.12677/AAM.2021.1010338

参考文献

[1] Hu, Z.L., Song, S., Xu, C.J., et al. (2020) Clinical Characteristics of 24 Asymptomatic Infections with COVID-19 Screened among Close Contacts in Nanjing, China. Science China Life Sciences, 63, 706-719. [Google Scholar] [CrossRef] [PubMed]
[2] Guo, Y.-R., Cao, Q.-D., Hong, Z.-S., et al. (2020) The Origin, Transmission and Clinical Therapies on Coronavirus Disease 2019 (COVID-19) Outbreak—An Update on the Status. Military Medical Research, 7, 93-103. [Google Scholar] [CrossRef] [PubMed]
[3] 曹盛力, 冯沛华, 时朋朋. 修正SEIR传染病动力学模型应用于湖北省2019冠状病毒病(COVID-19)疫情预测和评估[J]. 浙江大学学报(医学版), 2020, 49(2): 178-184.
[4] 李东辉, 郑三强, 杨淑伶. K-means聚类算法在SIR传染病模型中的应用研究[J]. 数学的实践与认识, 2021, 51(2): 268-276.
[5] 庞金彪, 鹿利. SIR型传染病模糊控制模型及其应用[J]. 中国卫生统计, 2003, 20(3): 154-157.
[6] 张艳霞, 李进. 基于SIR模型的新冠肺炎疫情传播预测分析[J]. 安徽工业大学学报(自然科学版), 2020, 37(1): 94-101.
[7] 范如国, 王奕博, 罗明, 张应青, 朱超平. 基于SEIR的新冠肺炎传播模型及拐点预测分析[J]. 电子科技大学学报, 2020, 49(3): 369-374.
[8] Giordano, G., Blanchini, F., Bruno, R., Colaneri, P., Filippo, A.D., Matteo, A.D. and Colaneri, M. (2020) Modelling the COVID-19 Epidemic and Implementation of Population-Wide Interventions in Italy. Nature Medicine, 26, 855-860. [Google Scholar] [CrossRef] [PubMed]
[9] Atangana, A. and Gómez-Aguilar, J. (2018) Fractional Derivatives with No-Index Law Property: Application to Chaos and Statistics. Chaos Solitons Fractals, 114, 516-535. [Google Scholar] [CrossRef] 
[10] Morales-Delgado, V.F., Gómez-Aguilar, J.F., Saad, K. and Jiménez, R.F.E. (2019) Application of the Caputo-Fabrizio and Atangana-Baleanu Fractional Derivatives to Mathematical Model of Cancer Chemotherapy Effect. Mathematical Methods in the Applied Sciences, 42, 1167-1193. [Google Scholar] [CrossRef] 
[11] Khan, M.A. and Atangana, A. (2020) Modeling the Dynamics of Novel Coronavirus (2019-nCov) with Fractional Derivative. Alexandria Engineering Journal, 59, 2379-2389. [Google Scholar] [CrossRef] 

为你推荐