A novel simulation-based analysis of a stochastic HIV model with the time delay using high order spectral collocation technique
Abstract The economic impact of Human Immunodeficiency Virus (HIV) goes beyond individual levels and it has a significant influence on communities and nations worldwide. Studying the transmission patterns in HIV dynamics is crucial for understanding the tracking behavior and informing policymakers a...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-04-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-57073-3 |
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| author | Sami Ullah Khan Saif Ullah Shuo Li Almetwally M. Mostafa Muhammad Bilal Riaz Nouf F. AlQahtani Shewafera Wondimagegnhu Teklu |
| author_facet | Sami Ullah Khan Saif Ullah Shuo Li Almetwally M. Mostafa Muhammad Bilal Riaz Nouf F. AlQahtani Shewafera Wondimagegnhu Teklu |
| author_sort | Sami Ullah Khan |
| collection | DOAJ |
| description | Abstract The economic impact of Human Immunodeficiency Virus (HIV) goes beyond individual levels and it has a significant influence on communities and nations worldwide. Studying the transmission patterns in HIV dynamics is crucial for understanding the tracking behavior and informing policymakers about the possible control of this viral infection. Various approaches have been adopted to explore how the virus interacts with the immune system. Models involving differential equations with delays have become prevalent across various scientific and technical domains over the past few decades. In this study, we present a novel mathematical model comprising a system of delay differential equations to describe the dynamics of intramural HIV infection. The model characterizes three distinct cell sub-populations and the HIV virus. By incorporating time delay between the viral entry into target cells and the subsequent production of new virions, our model provides a comprehensive understanding of the infection process. Our study focuses on investigating the stability of two crucial equilibrium states the infection-free and endemic equilibriums. To analyze the infection-free equilibrium, we utilize the LaSalle invariance principle. Further, we prove that if reproduction is less than unity, the disease free equilibrium is locally and globally asymptotically stable. To ensure numerical accuracy and preservation of essential properties from the continuous mathematical model, we use a spectral scheme having a higher-order accuracy. This scheme effectively captures the underlying dynamics and enables efficient numerical simulations. |
| first_indexed | 2024-04-24T12:39:27Z |
| format | Article |
| id | doaj.art-7557f93369b946a18013a825ea5f485d |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-04-24T12:39:27Z |
| publishDate | 2024-04-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-7557f93369b946a18013a825ea5f485d2024-04-07T11:18:40ZengNature PortfolioScientific Reports2045-23222024-04-0114111710.1038/s41598-024-57073-3A novel simulation-based analysis of a stochastic HIV model with the time delay using high order spectral collocation techniqueSami Ullah Khan0Saif Ullah1Shuo Li2Almetwally M. Mostafa3Muhammad Bilal Riaz4Nouf F. AlQahtani5Shewafera Wondimagegnhu Teklu6Department of Mathematics, City University of Science and Information TechnologyDepartment of Mathematics, University of PeshawarSchool of Mathematics and Data Sciences, Changji UniversityDepartment of Information Systems, College of Computers and Information Science, King Saud UniversityIT4Innovations, VSB- Technical University of OstravaIS Department, College of Education, King Saud UniversityDepartment of Mathematics, College of Natural and Computational Sciences, Debre Berhan UniversityAbstract The economic impact of Human Immunodeficiency Virus (HIV) goes beyond individual levels and it has a significant influence on communities and nations worldwide. Studying the transmission patterns in HIV dynamics is crucial for understanding the tracking behavior and informing policymakers about the possible control of this viral infection. Various approaches have been adopted to explore how the virus interacts with the immune system. Models involving differential equations with delays have become prevalent across various scientific and technical domains over the past few decades. In this study, we present a novel mathematical model comprising a system of delay differential equations to describe the dynamics of intramural HIV infection. The model characterizes three distinct cell sub-populations and the HIV virus. By incorporating time delay between the viral entry into target cells and the subsequent production of new virions, our model provides a comprehensive understanding of the infection process. Our study focuses on investigating the stability of two crucial equilibrium states the infection-free and endemic equilibriums. To analyze the infection-free equilibrium, we utilize the LaSalle invariance principle. Further, we prove that if reproduction is less than unity, the disease free equilibrium is locally and globally asymptotically stable. To ensure numerical accuracy and preservation of essential properties from the continuous mathematical model, we use a spectral scheme having a higher-order accuracy. This scheme effectively captures the underlying dynamics and enables efficient numerical simulations.https://doi.org/10.1038/s41598-024-57073-3HIV infectionMathematical delay modelStochastic effectStability analysisSpectral methodLegendre-Gauss-Lobatto points |
| spellingShingle | Sami Ullah Khan Saif Ullah Shuo Li Almetwally M. Mostafa Muhammad Bilal Riaz Nouf F. AlQahtani Shewafera Wondimagegnhu Teklu A novel simulation-based analysis of a stochastic HIV model with the time delay using high order spectral collocation technique Scientific Reports HIV infection Mathematical delay model Stochastic effect Stability analysis Spectral method Legendre-Gauss-Lobatto points |
| title | A novel simulation-based analysis of a stochastic HIV model with the time delay using high order spectral collocation technique |
| title_full | A novel simulation-based analysis of a stochastic HIV model with the time delay using high order spectral collocation technique |
| title_fullStr | A novel simulation-based analysis of a stochastic HIV model with the time delay using high order spectral collocation technique |
| title_full_unstemmed | A novel simulation-based analysis of a stochastic HIV model with the time delay using high order spectral collocation technique |
| title_short | A novel simulation-based analysis of a stochastic HIV model with the time delay using high order spectral collocation technique |
| title_sort | novel simulation based analysis of a stochastic hiv model with the time delay using high order spectral collocation technique |
| topic | HIV infection Mathematical delay model Stochastic effect Stability analysis Spectral method Legendre-Gauss-Lobatto points |
| url | https://doi.org/10.1038/s41598-024-57073-3 |
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