{"title":"通过 Pell-Lucas 配位算法对分数 COVID-19 模型进行数值求解和模拟","authors":"Gamze Yıldırım, Şuayip Yüzbaşı","doi":"10.1002/mma.10284","DOIUrl":null,"url":null,"abstract":"<p>The aim of this study is to present the evolution of COVID-19 pandemic in Turkey. For this, the SIR (Susceptible, Infected, Removed) model with the fractional order derivative is employed. By applying the collocation method via the Pell–Lucas polynomials (PLPs) to this model, the approximate solutions of model with fractional order derivative are obtained. Hence, the comments are made about the susceptible population, the infected population, and the recovered population. For the method, firstly, PLPs are expressed in matrix form for a selected number of \n<span></span><math>\n <semantics>\n <mrow>\n <mi>N</mi>\n </mrow>\n <annotation>$$ N $$</annotation>\n </semantics></math>. With the help of this matrix relationship, the matrix forms of each term in the SIR model with the fractional order derivative are constituted. For implementation and visualization, we utilize MATLAB. Moreover, the outcomes for the Runge–Kutta method (RKM) are obtained using MATLAB, and these results are compared with the results obtained with the Pell–Lucas collocation method (PLCM). From all simulations, it is concluded that the presented method is effective and reliable.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10284","citationCount":"0","resultStr":"{\"title\":\"Numerical solutions and simulations of the fractional COVID-19 model via Pell–Lucas collocation algorithm\",\"authors\":\"Gamze Yıldırım, Şuayip Yüzbaşı\",\"doi\":\"10.1002/mma.10284\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The aim of this study is to present the evolution of COVID-19 pandemic in Turkey. For this, the SIR (Susceptible, Infected, Removed) model with the fractional order derivative is employed. By applying the collocation method via the Pell–Lucas polynomials (PLPs) to this model, the approximate solutions of model with fractional order derivative are obtained. Hence, the comments are made about the susceptible population, the infected population, and the recovered population. For the method, firstly, PLPs are expressed in matrix form for a selected number of \\n<span></span><math>\\n <semantics>\\n <mrow>\\n <mi>N</mi>\\n </mrow>\\n <annotation>$$ N $$</annotation>\\n </semantics></math>. With the help of this matrix relationship, the matrix forms of each term in the SIR model with the fractional order derivative are constituted. For implementation and visualization, we utilize MATLAB. Moreover, the outcomes for the Runge–Kutta method (RKM) are obtained using MATLAB, and these results are compared with the results obtained with the Pell–Lucas collocation method (PLCM). From all simulations, it is concluded that the presented method is effective and reliable.</p>\",\"PeriodicalId\":49865,\"journal\":{\"name\":\"Mathematical Methods in the Applied Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-07-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10284\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Methods in the Applied Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mma.10284\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10284","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Numerical solutions and simulations of the fractional COVID-19 model via Pell–Lucas collocation algorithm
The aim of this study is to present the evolution of COVID-19 pandemic in Turkey. For this, the SIR (Susceptible, Infected, Removed) model with the fractional order derivative is employed. By applying the collocation method via the Pell–Lucas polynomials (PLPs) to this model, the approximate solutions of model with fractional order derivative are obtained. Hence, the comments are made about the susceptible population, the infected population, and the recovered population. For the method, firstly, PLPs are expressed in matrix form for a selected number of
. With the help of this matrix relationship, the matrix forms of each term in the SIR model with the fractional order derivative are constituted. For implementation and visualization, we utilize MATLAB. Moreover, the outcomes for the Runge–Kutta method (RKM) are obtained using MATLAB, and these results are compared with the results obtained with the Pell–Lucas collocation method (PLCM). From all simulations, it is concluded that the presented method is effective and reliable.
期刊介绍：
Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted.
Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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