Mathematical model of SIR epidemic system (COVID-19) with fractional derivative: stability and numerical analysis.

IF 4.1 3区数学 Q1 Mathematics

Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-01-04 DOI:10.1186/s13662-020-03192-w

Rubayyi T Alqahtani

{"title":"Mathematical model of SIR epidemic system (COVID-19) with fractional derivative: stability and numerical analysis.","authors":"Rubayyi T Alqahtani","doi":"10.1186/s13662-020-03192-w","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, we study and analyze the susceptible-infectious-removed (SIR) dynamics considering the effect of health system. We consider a general incidence rate function and the recovery rate as functions of the number of hospital beds. We prove the existence, uniqueness, and boundedness of the model. We investigate all possible steady-state solutions of the model and their stability. The analysis shows that the free steady state is locally stable when the basic reproduction number <math><msub><mi>R</mi> <mn>0</mn></msub> </math> is less than unity and unstable when <math><msub><mi>R</mi> <mn>0</mn></msub> <mo>></mo> <mn>1</mn></math> . The analysis shows that the phenomenon of backward bifurcation occurs when <math><msub><mi>R</mi> <mn>0</mn></msub> <mo><</mo> <mn>1</mn></math> . Then we investigate the model using the concept of fractional differential operator. Finally, we perform numerical simulations to illustrate the theoretical analysis and study the effect of the parameters on the model for various fractional orders.</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://www.ncbi.nlm.nih.gov/pmc/articles/PMC7779337/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Difference Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13662-020-03192-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2021/1/4 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

Abstract

In this paper, we study and analyze the susceptible-infectious-removed (SIR) dynamics considering the effect of health system. We consider a general incidence rate function and the recovery rate as functions of the number of hospital beds. We prove the existence, uniqueness, and boundedness of the model. We investigate all possible steady-state solutions of the model and their stability. The analysis shows that the free steady state is locally stable when the basic reproduction number $R_{0}$ is less than unity and unstable when $R_{0} > 1$ . The analysis shows that the phenomenon of backward bifurcation occurs when $R_{0} < 1$ . Then we investigate the model using the concept of fractional differential operator. Finally, we perform numerical simulations to illustrate the theoretical analysis and study the effect of the parameters on the model for various fractional orders.

Abstract Image

查看原文本刊更多论文

带分数导数的 SIR 流行病系统 (COVID-19) 数学模型：稳定性与数值分析。

在本文中，我们研究并分析了考虑到卫生系统影响的易感-感染-移除（SIR）动态。我们将一般发病率函数和康复率视为医院床位数的函数。我们证明了模型的存在性、唯一性和有界性。我们研究了模型所有可能的稳态解及其稳定性。分析表明，当基本繁殖数 R 0 小于 1 时，自由稳态是局部稳定的；当 R 0 > 1 时，自由稳态是不稳定的。分析表明，当 R 0 1 时会出现向后分叉现象。然后，我们利用分数微分算子的概念对模型进行了研究。最后，我们进行了数值模拟以说明理论分析，并研究了不同分数阶数下参数对模型的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Advances in Difference Equations 数学-数学

自引率

0.00%

发文量

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.