优化分数阶下COVID-19的Caputo SIR模型。

IF 4.1 3区 数学 Q1 Mathematics
Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-03-24 DOI:10.1186/s13662-021-03345-5
Ali S Alshomrani, Malik Z Ullah, Dumitru Baleanu
{"title":"优化分数阶下COVID-19的Caputo SIR模型。","authors":"Ali S Alshomrani,&nbsp;Malik Z Ullah,&nbsp;Dumitru Baleanu","doi":"10.1186/s13662-021-03345-5","DOIUrl":null,"url":null,"abstract":"<p><p>Everyone is talking about coronavirus from the last couple of months due to its exponential spread throughout the globe. Lives have become paralyzed, and as many as 180 countries have been so far affected with 928,287 (14 September 2020) deaths within a couple of months. Ironically, 29,185,779 are still active cases. Having seen such a drastic situation, a relatively simple epidemiological SIR model with Caputo derivative is suggested unlike more sophisticated models being proposed nowadays in the current literature. The major aim of the present research study is to look for possibilities and extents to which the SIR model fits the real data for the cases chosen from 1 April to 15 March 2020, Pakistan. To further analyze qualitative behavior of the Caputo SIR model, uniqueness conditions under the Banach contraction principle are discussed and stability analysis with basic reproduction number is investigated using Ulam-Hyers and its generalized version. The best parameters have been obtained via the nonlinear least-squares curve fitting technique. The infectious compartment of the Caputo SIR model fits the real data better than the classical version of the SIR model (Brauer et al. in Mathematical Models in Epidemiology 2019). Average absolute relative error under the Caputo operator is about 48% smaller than the one obtained in the classical case ( <math><mi>ν</mi> <mo>=</mo> <mn>1</mn></math> ). Time series and 3D contour plots offer social distancing to be the most effective measure to control the epidemic.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":null,"pages":null},"PeriodicalIF":4.1000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-021-03345-5","citationCount":"22","resultStr":"{\"title\":\"Caputo SIR model for COVID-19 under optimized fractional order.\",\"authors\":\"Ali S Alshomrani,&nbsp;Malik Z Ullah,&nbsp;Dumitru Baleanu\",\"doi\":\"10.1186/s13662-021-03345-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>Everyone is talking about coronavirus from the last couple of months due to its exponential spread throughout the globe. Lives have become paralyzed, and as many as 180 countries have been so far affected with 928,287 (14 September 2020) deaths within a couple of months. Ironically, 29,185,779 are still active cases. Having seen such a drastic situation, a relatively simple epidemiological SIR model with Caputo derivative is suggested unlike more sophisticated models being proposed nowadays in the current literature. The major aim of the present research study is to look for possibilities and extents to which the SIR model fits the real data for the cases chosen from 1 April to 15 March 2020, Pakistan. To further analyze qualitative behavior of the Caputo SIR model, uniqueness conditions under the Banach contraction principle are discussed and stability analysis with basic reproduction number is investigated using Ulam-Hyers and its generalized version. The best parameters have been obtained via the nonlinear least-squares curve fitting technique. The infectious compartment of the Caputo SIR model fits the real data better than the classical version of the SIR model (Brauer et al. in Mathematical Models in Epidemiology 2019). Average absolute relative error under the Caputo operator is about 48% smaller than the one obtained in the classical case ( <math><mi>ν</mi> <mo>=</mo> <mn>1</mn></math> ). Time series and 3D contour plots offer social distancing to be the most effective measure to control the epidemic.</p>\",\"PeriodicalId\":53311,\"journal\":{\"name\":\"Advances in Difference Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.1000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1186/s13662-021-03345-5\",\"citationCount\":\"22\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Difference Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1186/s13662-021-03345-5\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2021/3/24 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Difference Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13662-021-03345-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2021/3/24 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 22

摘要

由于冠状病毒在全球的指数传播,每个人都在谈论过去几个月的冠状病毒。迄今为止,已有多达180个国家受到影响,在几个月内死亡928,287人(2020年9月14日)。具有讽刺意味的是,29185779件案件仍在审理中。看到这种极端的情况,我们提出了一个相对简单的带有Caputo导数的流行病学SIR模型,而不是目前文献中提出的更复杂的模型。本研究的主要目的是寻找SIR模型适合巴基斯坦2020年4月1日至3月15日所选病例的实际数据的可能性和程度。为了进一步分析Caputo SIR模型的定性行为,讨论了Banach收缩原理下的唯一性条件,并利用Ulam-Hyers及其广义版本研究了具有基本再现数的稳定性分析。通过非线性最小二乘曲线拟合技术得到了最佳参数。Caputo SIR模型的感染区比经典版本的SIR模型更符合真实数据(Brauer et al. in Epidemiology 2019)。在Caputo算子下的平均绝对相对误差比经典情况(ν = 1)下的平均绝对相对误差小48%左右。时间序列和三维等高线图表明,保持社会距离是控制疫情的最有效措施。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Caputo SIR model for COVID-19 under optimized fractional order.

Caputo SIR model for COVID-19 under optimized fractional order.

Caputo SIR model for COVID-19 under optimized fractional order.

Caputo SIR model for COVID-19 under optimized fractional order.

Everyone is talking about coronavirus from the last couple of months due to its exponential spread throughout the globe. Lives have become paralyzed, and as many as 180 countries have been so far affected with 928,287 (14 September 2020) deaths within a couple of months. Ironically, 29,185,779 are still active cases. Having seen such a drastic situation, a relatively simple epidemiological SIR model with Caputo derivative is suggested unlike more sophisticated models being proposed nowadays in the current literature. The major aim of the present research study is to look for possibilities and extents to which the SIR model fits the real data for the cases chosen from 1 April to 15 March 2020, Pakistan. To further analyze qualitative behavior of the Caputo SIR model, uniqueness conditions under the Banach contraction principle are discussed and stability analysis with basic reproduction number is investigated using Ulam-Hyers and its generalized version. The best parameters have been obtained via the nonlinear least-squares curve fitting technique. The infectious compartment of the Caputo SIR model fits the real data better than the classical version of the SIR model (Brauer et al. in Mathematical Models in Epidemiology 2019). Average absolute relative error under the Caputo operator is about 48% smaller than the one obtained in the classical case ( ν = 1 ). Time series and 3D contour plots offer social distancing to be the most effective measure to control the epidemic.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
审稿时长
4-8 weeks
期刊介绍: The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信