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Role of Vaccines in Controlling the Spread of COVID-19: A Fractional-Order Model
In this paper, we present a fractional-order mathematical model in the Caputo sense to investigate the significance of vaccines in controlling COVID-19. The Banach contraction mapping principle is used to prove the existence and uniqueness of the solution. Based on the magnitude of the basic reprodu...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2023
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9861806/ https://www.ncbi.nlm.nih.gov/pubmed/36679990 http://dx.doi.org/10.3390/vaccines11010145 |
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author | Baba, Isa Abdullahi Humphries, Usa Wannasingha Rihan, Fathalla A. |
author_facet | Baba, Isa Abdullahi Humphries, Usa Wannasingha Rihan, Fathalla A. |
author_sort | Baba, Isa Abdullahi |
collection | PubMed |
description | In this paper, we present a fractional-order mathematical model in the Caputo sense to investigate the significance of vaccines in controlling COVID-19. The Banach contraction mapping principle is used to prove the existence and uniqueness of the solution. Based on the magnitude of the basic reproduction number, we show that the model consists of two equilibrium solutions that are stable. The disease-free and endemic equilibrium points are locally stably when [Formula: see text] and [Formula: see text] respectively. We perform numerical simulations, with the significance of the vaccine clearly shown. The changes that occur due to the variation of the fractional order [Formula: see text] are also shown. The model has been validated by fitting it to four months of real COVID-19 infection data in Thailand. Predictions for a longer period are provided by the model, which provides a good fit for the data. |
format | Online Article Text |
id | pubmed-9861806 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-98618062023-01-22 Role of Vaccines in Controlling the Spread of COVID-19: A Fractional-Order Model Baba, Isa Abdullahi Humphries, Usa Wannasingha Rihan, Fathalla A. Vaccines (Basel) Article In this paper, we present a fractional-order mathematical model in the Caputo sense to investigate the significance of vaccines in controlling COVID-19. The Banach contraction mapping principle is used to prove the existence and uniqueness of the solution. Based on the magnitude of the basic reproduction number, we show that the model consists of two equilibrium solutions that are stable. The disease-free and endemic equilibrium points are locally stably when [Formula: see text] and [Formula: see text] respectively. We perform numerical simulations, with the significance of the vaccine clearly shown. The changes that occur due to the variation of the fractional order [Formula: see text] are also shown. The model has been validated by fitting it to four months of real COVID-19 infection data in Thailand. Predictions for a longer period are provided by the model, which provides a good fit for the data. MDPI 2023-01-09 /pmc/articles/PMC9861806/ /pubmed/36679990 http://dx.doi.org/10.3390/vaccines11010145 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Baba, Isa Abdullahi Humphries, Usa Wannasingha Rihan, Fathalla A. Role of Vaccines in Controlling the Spread of COVID-19: A Fractional-Order Model |
title | Role of Vaccines in Controlling the Spread of COVID-19: A Fractional-Order Model |
title_full | Role of Vaccines in Controlling the Spread of COVID-19: A Fractional-Order Model |
title_fullStr | Role of Vaccines in Controlling the Spread of COVID-19: A Fractional-Order Model |
title_full_unstemmed | Role of Vaccines in Controlling the Spread of COVID-19: A Fractional-Order Model |
title_short | Role of Vaccines in Controlling the Spread of COVID-19: A Fractional-Order Model |
title_sort | role of vaccines in controlling the spread of covid-19: a fractional-order model |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9861806/ https://www.ncbi.nlm.nih.gov/pubmed/36679990 http://dx.doi.org/10.3390/vaccines11010145 |
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