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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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-12-01
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| 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. |
| format | Article |
| id | doaj-art-66d0d746f13b4f08b90370763053f0f4 |
| institution | OA Journals |
| issn | 1387-3954 1744-5051 |
| language | English |
| 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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