A Pell–Lucas Collocation Approach for an SIR Model on the Spread of the Novel Coronavirus (SARS CoV-2) Pandemic: The Case of Turkey

Şuayip Yüzbaşı () and Gamze Yıldırım
Additional contact information
Şuayip Yüzbaşı: Department of Mathematics, Faculty of Science, Akdeniz University, Antalya 07058, Turkey
Gamze Yıldırım: Department of Mathematics, Faculty of Science, Akdeniz University, Antalya 07058, Turkey

Mathematics, 2023, vol. 11, issue 3, 1-22

Abstract: In this article, we present a study about the evolution of the COVID-19 pandemic in Turkey. The modelling of a new virus named SARS-CoV-2 is considered by an SIR model consisting of a nonlinear system of differential equations. A collocation approach based on the Pell–Lucas polynomials is studied to get the approximate solutions of this model. First, the approximate solution in forms of the truncated Pell–Lucas polynomials are written in matrix forms. By utilizing the collocation points and the matrix relations, the considered model is converted to a system of the nonlinear algebraic equations. By solving this system, the unknown coefficients of the assumed Pell–Lucas polynomial solutions are determined, and so the approximate solutions are obtained. Secondly, two theorems about the error analysis are given and proved. The applications of the methods are made by using a code written in MATLAB. The parameters and the initial conditions of the model are determined according to the reported data from the Turkey Ministry of Health. Finally, the approximate solutions and the absolute error functions are visualized. To demonstrate the effectiveness of the method, our approximate solutions are compared with the approximate solutions obtained by the Runge–Kutta method. The reliable results are obtained from numerical results and comparisons. Thanks to this study, the tendencies of the pandemic can be estimated. In addition, the method can be applied to other countries after some necessary arrangements.

Keywords: collocation method; COVID-19 modeling; error analysis; mathematical modeling; nonlinear differential equations; Pell–Lucas polynomials; SIR model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/3/697/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/3/697/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:3:p:697-:d:1051084

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().