<abstract xmlns="http://www.w3.org/1999/xhtml">
<p>This study presents the problem of spreading non fatal disease in a population by using the Morgan-Voyce collocation method. The main aim of this paper is to find the exact solutions of the SIR model with vaccination. The problem may be modelled mathematically with a nonlinear system of ordinary differential equations. The presented method reduces the problem into a nonlinear algebraic system of equations by using unknown coefficient Morgan-Voyce polynomials and expanding approximate solutions. Morgan-Voyce polynomials are used. These unknown coefficients are calculated via the collocation method and matrix operation derivations. Two examples are given to show the feasibility of the method. To calculate the solutions, MATLAB R2021a is used. Additionally, comparing our method to the Homotopy perturbation method (HPM) and the Laplace Adomian decomposition method (LADM) proves the accuracy of the solution. The method studied can be seen as effective from these comparisons. So, it is essential to find solutions for the governing model. The study will contribute to literature since we also discuss the vaccination situation. The results of this study are valuable for controlling an epidemic.</p>
</abstract>

This study presents the problem of spreading non fatal disease in a population by using the Morgan-Voyce collocation method. The main aim of this paper is to find the exact solutions of the SIR model with vaccination. The problem may be modelled mathematically with a nonlinear system of ordinary differential equations. The presented method reduces the problem into a nonlinear algebraic system of equations by using unknown coefficient Morgan-Voyce polynomials and expanding approximate solutions. Morgan-Voyce polynomials are used. These unknown coefficients are calculated via the collocation method and matrix operation derivations. Two examples are given to show the feasibility of the method. To calculate the solutions, MATLAB R2021a is used. Additionally, comparing our method to the Homotopy perturbation method (HPM) and the Laplace Adomian decomposition method (LADM) proves the accuracy of the solution. The method studied can be seen as effective from these comparisons. So, it is essential to find solutions for the governing model. The study will contribute to literature since we also discuss the vaccination situation. The results of this study are valuable for controlling an epidemic.

A numerical approach for an epidemic SIR model via Morgan-Voyce series

Faculty of Sciences, Department of Mathematics

International Journal of Mathematics and Computer in Engineering

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"A numerical approach for an epidemic SIR model via Morgan-Voyce series"}

This study presents the problem of spreading non fatal disease in a population by using the Morgan-Voyce collocation method. The main aim of this paper is to...

A numerical approach for an epidemic SIR model via Morgan-Voyce series

Article Category: Review Study

Publié en ligne: 31 oct. 2023

Pages: 125 - 140

Reçu: 03 août 2023

Accepté: 11 sept. 2023

DOI: https://doi.org/10.2478/ijmce-2024-0010

Mots clés
SIR model with vaccine, Morgan-Voyce polynomials, collocation points, epidemic model

© 2024 Özgül İlhan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

A numerical approach for an epidemic SIR model via Morgan-Voyce series

Article Category: Review Study

Publié en ligne: 31 oct. 2023

Pages: 125 - 140

Reçu: 03 août 2023

Accepté: 11 sept. 2023

DOI: https://doi.org/10.2478/ijmce-2024-0010

Mots clésSIR model with vaccine, Morgan-Voyce polynomials, collocation points, epidemic model

© 2024 Özgül İlhan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Mots clés
SIR model with vaccine, Morgan-Voyce polynomials, collocation points, epidemic model