Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay
This study is concerned with finding a numerical solution to the delay epidemic model with diffusion. This is not a simple task as variables involved in the model exhibit some important physical features. We have therefore designed an efficient numerical scheme that preserves the properties acquired...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2020-01-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/article/10.3389/fphy.2019.00229/full |
| _version_ | 1818152153448972288 |
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| author | Muhammad Jawaz Muhammad Jawaz Nauman Ahmed Nauman Ahmed Dumitru Baleanu Dumitru Baleanu Muhammad Rafiq Muhammad Aziz-ur Rehman |
| author_facet | Muhammad Jawaz Muhammad Jawaz Nauman Ahmed Nauman Ahmed Dumitru Baleanu Dumitru Baleanu Muhammad Rafiq Muhammad Aziz-ur Rehman |
| author_sort | Muhammad Jawaz |
| collection | DOAJ |
| description | This study is concerned with finding a numerical solution to the delay epidemic model with diffusion. This is not a simple task as variables involved in the model exhibit some important physical features. We have therefore designed an efficient numerical scheme that preserves the properties acquired by the given system. We also further develop Euler's technique for a delayed epidemic reaction–diffusion model. The proposed numerical technique is also compared with the forward Euler technique, and we observe that the forward Euler technique demonstrates the false behavior at certain step sizes. On the other hand, the proposed technique preserves the true behavior of the continuous system at all step sizes. Furthermore, the effect of the delay factor is discussed graphically by using the proposed technique. |
| first_indexed | 2024-12-11T13:50:12Z |
| format | Article |
| id | doaj.art-b79e662201084524a24f4b2363ed1a93 |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-12-11T13:50:12Z |
| publishDate | 2020-01-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-b79e662201084524a24f4b2363ed1a932022-12-22T01:04:19ZengFrontiers Media S.A.Frontiers in Physics2296-424X2020-01-01710.3389/fphy.2019.00229500315Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time DelayMuhammad Jawaz0Muhammad Jawaz1Nauman Ahmed2Nauman Ahmed3Dumitru Baleanu4Dumitru Baleanu5Muhammad Rafiq6Muhammad Aziz-ur Rehman7Department of Mathematics, University of Management and Technology, Lahore, PakistanDepartment of Mathematics and Statistics, The University of Lahore, Lahore, PakistanDepartment of Mathematics, University of Management and Technology, Lahore, PakistanDepartment of Mathematics and Statistics, The University of Lahore, Lahore, PakistanDepartment of Mathematics, Cankaya University, Ankara, TurkeyInstitute of Space Sciences, Bucharest, RomaniaFaculty of Engineering, University of Central Punjab, Lahore, PakistanDepartment of Mathematics, University of Management and Technology, Lahore, PakistanThis study is concerned with finding a numerical solution to the delay epidemic model with diffusion. This is not a simple task as variables involved in the model exhibit some important physical features. We have therefore designed an efficient numerical scheme that preserves the properties acquired by the given system. We also further develop Euler's technique for a delayed epidemic reaction–diffusion model. The proposed numerical technique is also compared with the forward Euler technique, and we observe that the forward Euler technique demonstrates the false behavior at certain step sizes. On the other hand, the proposed technique preserves the true behavior of the continuous system at all step sizes. Furthermore, the effect of the delay factor is discussed graphically by using the proposed technique.https://www.frontiersin.org/article/10.3389/fphy.2019.00229/fullepidemic model with diffusiontime delayHIV/AIDS (acquired immunodeficiency syndrome)positivityfinite difference methodsimulations |
| spellingShingle | Muhammad Jawaz Muhammad Jawaz Nauman Ahmed Nauman Ahmed Dumitru Baleanu Dumitru Baleanu Muhammad Rafiq Muhammad Aziz-ur Rehman Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay Frontiers in Physics epidemic model with diffusion time delay HIV/AIDS (acquired immunodeficiency syndrome) positivity finite difference method simulations |
| title | Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay |
| title_full | Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay |
| title_fullStr | Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay |
| title_full_unstemmed | Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay |
| title_short | Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay |
| title_sort | positivity preserving technique for the solution of hiv aids reaction diffusion model with time delay |
| topic | epidemic model with diffusion time delay HIV/AIDS (acquired immunodeficiency syndrome) positivity finite difference method simulations |
| url | https://www.frontiersin.org/article/10.3389/fphy.2019.00229/full |
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