Local and global stability analysis of HIV/AIDS by using a nonstandard finite difference scheme
Abstract This study presents a mathematical model incorporating both asymptomatic and symptomatic HIV-infected individuals to analyze the dynamics of HIV/AIDS. This expanded model offers a more comprehensive understanding of the epidemic’s spread. We calculate the basic reproduction number (R0) to q...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-02-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-82872-z |
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| author | Amjid Hussain Morani Maha Mohammed Saeed Muhammad Aslam Atif Mehmoud Ali Shokri Herbert Mukalazi |
| author_facet | Amjid Hussain Morani Maha Mohammed Saeed Muhammad Aslam Atif Mehmoud Ali Shokri Herbert Mukalazi |
| author_sort | Amjid Hussain Morani |
| collection | DOAJ |
| description | Abstract This study presents a mathematical model incorporating both asymptomatic and symptomatic HIV-infected individuals to analyze the dynamics of HIV/AIDS. This expanded model offers a more comprehensive understanding of the epidemic’s spread. We calculate the basic reproduction number (R0) to quantify the virus’s transmission potential. To achieve accurate and robust simulations, we introduce the Nonstandard Finite Difference Scheme (NSFD). Compared to traditional methods like RK-4, NSFD offers improved dynamical consistency and numerical precision, leading to enhanced stability and efficiency in simulating infectious diseases like HIV/AIDS. Local and global stability analysis are performed using the Routh-Hurwitz method. The NSFD method effectively captures the dynamics of HIV propagation under various scenarios, providing valuable insights into HIV/AIDS progression. We demonstrate the superiority of the NSFD approach compared to existing methods, paving the way for further research in modeling viral infections. |
| format | Article |
| id | doaj-art-c193adc081964f0da3471c92f3b8665f |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-c193adc081964f0da3471c92f3b8665f2025-02-09T12:29:56ZengNature PortfolioScientific Reports2045-23222025-02-0115111210.1038/s41598-024-82872-zLocal and global stability analysis of HIV/AIDS by using a nonstandard finite difference schemeAmjid Hussain Morani0Maha Mohammed Saeed1Muhammad Aslam2Atif Mehmoud3Ali Shokri4Herbert Mukalazi5Department of Mathematics, Institute of Numerical Sciences, Gomal UniversityDepartment of Mathematics, Faculty of Sciences, King Abdulaziz UniversityDepartment of Mathematics, College of Sciences, King Khalid UniversityDepartment of Mathematics, Faculty of Sciences, King Abdulaziz UniversityDepartment of Mathematics, Faculty of Science, University of MaraghehDepartment of Mathematics and Statistics, Kyambogo UniversityAbstract This study presents a mathematical model incorporating both asymptomatic and symptomatic HIV-infected individuals to analyze the dynamics of HIV/AIDS. This expanded model offers a more comprehensive understanding of the epidemic’s spread. We calculate the basic reproduction number (R0) to quantify the virus’s transmission potential. To achieve accurate and robust simulations, we introduce the Nonstandard Finite Difference Scheme (NSFD). Compared to traditional methods like RK-4, NSFD offers improved dynamical consistency and numerical precision, leading to enhanced stability and efficiency in simulating infectious diseases like HIV/AIDS. Local and global stability analysis are performed using the Routh-Hurwitz method. The NSFD method effectively captures the dynamics of HIV propagation under various scenarios, providing valuable insights into HIV/AIDS progression. We demonstrate the superiority of the NSFD approach compared to existing methods, paving the way for further research in modeling viral infections.https://doi.org/10.1038/s41598-024-82872-zHIV/AIDSAsymptomatic infectionNonstandard finite difference scheme (NSFD)Basic reproduction numberLocal and global stability analysis |
| spellingShingle | Amjid Hussain Morani Maha Mohammed Saeed Muhammad Aslam Atif Mehmoud Ali Shokri Herbert Mukalazi Local and global stability analysis of HIV/AIDS by using a nonstandard finite difference scheme Scientific Reports HIV/AIDS Asymptomatic infection Nonstandard finite difference scheme (NSFD) Basic reproduction number Local and global stability analysis |
| title | Local and global stability analysis of HIV/AIDS by using a nonstandard finite difference scheme |
| title_full | Local and global stability analysis of HIV/AIDS by using a nonstandard finite difference scheme |
| title_fullStr | Local and global stability analysis of HIV/AIDS by using a nonstandard finite difference scheme |
| title_full_unstemmed | Local and global stability analysis of HIV/AIDS by using a nonstandard finite difference scheme |
| title_short | Local and global stability analysis of HIV/AIDS by using a nonstandard finite difference scheme |
| title_sort | local and global stability analysis of hiv aids by using a nonstandard finite difference scheme |
| topic | HIV/AIDS Asymptomatic infection Nonstandard finite difference scheme (NSFD) Basic reproduction number Local and global stability analysis |
| url | https://doi.org/10.1038/s41598-024-82872-z |
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