Computational approaches on integrating vaccination and treatment strategies in the SIR model using Galerkin time discretization scheme

In this manuscript, we carried out a thorough analysis of the general SIR model for epidemics. We broadened the model to include vaccination, treatment, and incidence rate. The vaccination rate is a testament to the alternatives made by individuals when it comes to receiving vaccinations and merging...

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Main Authors: Attaullah, Khaled Mahdi, Mehmet Yavuz, Salah Boulaaras, Mohamed Haiour, Viet-Thanh Pham
Format: Article
Language:English
Published: Taylor & Francis Group 2024-12-01
Series:Mathematical and Computer Modelling of Dynamical Systems
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Online Access:https://www.tandfonline.com/doi/10.1080/13873954.2024.2405504
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author Attaullah
Khaled Mahdi
Mehmet Yavuz
Salah Boulaaras
Mohamed Haiour
Viet-Thanh Pham
author_facet Attaullah
Khaled Mahdi
Mehmet Yavuz
Salah Boulaaras
Mohamed Haiour
Viet-Thanh Pham
author_sort Attaullah
collection DOAJ
description In this manuscript, we carried out a thorough analysis of the general SIR model for epidemics. We broadened the model to include vaccination, treatment, and incidence rate. The vaccination rate is a testament to the alternatives made by individuals when it comes to receiving vaccinations and merging with the community of the recovered. The treatment rate measures how often people who have contracted a disease are able to transition into the recovered category. The continuous Galerkin-Petrov method, specifically the cGP(2)-method, is employed to calculate the numerical solutions of the models. The cGP(2)-method imperative to analyse two unknowns over every time interval. The unknowns can be determined by solving a block system of size (2 × 2). This approach demonstrates a strong level of precision throughout the entire time interval, with an impressive rate of convergence at the discrete time points. In addition, the article investigates the concept of the basic reproduction number ([Formula: see text]) and explores the intricacies of conducting sensitivity analysis of the developed system.
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issn 1387-3954
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publishDate 2024-12-01
publisher Taylor & Francis Group
record_format Article
series Mathematical and Computer Modelling of Dynamical Systems
spelling doaj-art-66d0d746f13b4f08b90370763053f0f42025-08-20T02:34:31ZengTaylor & Francis GroupMathematical and Computer Modelling of Dynamical Systems1387-39541744-50512024-12-0130175879110.1080/13873954.2024.2405504Computational approaches on integrating vaccination and treatment strategies in the SIR model using Galerkin time discretization schemeAttaullah0Khaled Mahdi1Mehmet Yavuz2Salah Boulaaras3Mohamed Haiour4Viet-Thanh Pham5Department of Mathematics & Statistics, University of Chitral, Chitral, KP, PakistanDepartment of Physics, Faculty of Sciences, M’Sila University, M’Sila, AlgeriaDepartment of Mathematics and Computer Sciences, Necmettin Erbakan University, Konya, TürkiyeDepartment of Mathematics, College of Science, Qassim University, Buraydah, Saudi ArabiaNumerical Analysis, Optimization and Statistics Laboratory, University Badji Mokhtar, Annaba, AlgeriaFaculty of Electronics Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City, VietnamIn this manuscript, we carried out a thorough analysis of the general SIR model for epidemics. We broadened the model to include vaccination, treatment, and incidence rate. The vaccination rate is a testament to the alternatives made by individuals when it comes to receiving vaccinations and merging with the community of the recovered. The treatment rate measures how often people who have contracted a disease are able to transition into the recovered category. The continuous Galerkin-Petrov method, specifically the cGP(2)-method, is employed to calculate the numerical solutions of the models. The cGP(2)-method imperative to analyse two unknowns over every time interval. The unknowns can be determined by solving a block system of size (2 × 2). This approach demonstrates a strong level of precision throughout the entire time interval, with an impressive rate of convergence at the discrete time points. In addition, the article investigates the concept of the basic reproduction number ([Formula: see text]) and explores the intricacies of conducting sensitivity analysis of the developed system.https://www.tandfonline.com/doi/10.1080/13873954.2024.2405504SIR modelvaccination and treatment controlnumerical methodnumerical methoddynamical behaviornumerical methods
spellingShingle Attaullah
Khaled Mahdi
Mehmet Yavuz
Salah Boulaaras
Mohamed Haiour
Viet-Thanh Pham
Computational approaches on integrating vaccination and treatment strategies in the SIR model using Galerkin time discretization scheme
Mathematical and Computer Modelling of Dynamical Systems
SIR model
vaccination and treatment control
numerical method
numerical method
dynamical behavior
numerical methods
title Computational approaches on integrating vaccination and treatment strategies in the SIR model using Galerkin time discretization scheme
title_full Computational approaches on integrating vaccination and treatment strategies in the SIR model using Galerkin time discretization scheme
title_fullStr Computational approaches on integrating vaccination and treatment strategies in the SIR model using Galerkin time discretization scheme
title_full_unstemmed Computational approaches on integrating vaccination and treatment strategies in the SIR model using Galerkin time discretization scheme
title_short Computational approaches on integrating vaccination and treatment strategies in the SIR model using Galerkin time discretization scheme
title_sort computational approaches on integrating vaccination and treatment strategies in the sir model using galerkin time discretization scheme
topic SIR model
vaccination and treatment control
numerical method
numerical method
dynamical behavior
numerical methods
url https://www.tandfonline.com/doi/10.1080/13873954.2024.2405504
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AT mehmetyavuz computationalapproachesonintegratingvaccinationandtreatmentstrategiesinthesirmodelusinggalerkintimediscretizationscheme
AT salahboulaaras computationalapproachesonintegratingvaccinationandtreatmentstrategiesinthesirmodelusinggalerkintimediscretizationscheme
AT mohamedhaiour computationalapproachesonintegratingvaccinationandtreatmentstrategiesinthesirmodelusinggalerkintimediscretizationscheme
AT vietthanhpham computationalapproachesonintegratingvaccinationandtreatmentstrategiesinthesirmodelusinggalerkintimediscretizationscheme