Global Dynamics of Secondary DENV Infection with Diffusion
During the past eras, many mathematicians have paid their attentions to model the dynamics of dengue virus (DENV) infection but without taking into account the mobility of the cells and DENV particles. In this study, we develop and investigate a partial differential equations (PDEs) model that descr...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5585175 |
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| author | A. M. Elaiw A. S. Alofi |
| author_facet | A. M. Elaiw A. S. Alofi |
| author_sort | A. M. Elaiw |
| collection | DOAJ |
| description | During the past eras, many mathematicians have paid their attentions to model the dynamics of dengue virus (DENV) infection but without taking into account the mobility of the cells and DENV particles. In this study, we develop and investigate a partial differential equations (PDEs) model that describes the dynamics of secondary DENV infection taking into account the spatial mobility of DENV particles and cells. The model includes five nonlinear PDEs describing the interaction among the target cells, DENV-infected cells, DENV particles, heterologous antibodies, and homologous antibodies. In the beginning, the well-posedness of solutions, including the existence of global solutions and the boundedness, is justified. We derive three threshold parameters which govern the existence and stability of the four equilibria of the model. We study the global stability of all equilibria based on the construction of suitable Lyapunov functions and usage of Lyapunov–LaSalle’s invariance principle (LLIP). Last, numerical simulations are carried out in order to verify the validity of our theoretical results. |
| format | Article |
| id | doaj-art-5d39eec253704b0fa03db5bd8b94bdda |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-5d39eec253704b0fa03db5bd8b94bdda2025-02-03T01:04:17ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55851755585175Global Dynamics of Secondary DENV Infection with DiffusionA. M. Elaiw0A. S. Alofi1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDuring the past eras, many mathematicians have paid their attentions to model the dynamics of dengue virus (DENV) infection but without taking into account the mobility of the cells and DENV particles. In this study, we develop and investigate a partial differential equations (PDEs) model that describes the dynamics of secondary DENV infection taking into account the spatial mobility of DENV particles and cells. The model includes five nonlinear PDEs describing the interaction among the target cells, DENV-infected cells, DENV particles, heterologous antibodies, and homologous antibodies. In the beginning, the well-posedness of solutions, including the existence of global solutions and the boundedness, is justified. We derive three threshold parameters which govern the existence and stability of the four equilibria of the model. We study the global stability of all equilibria based on the construction of suitable Lyapunov functions and usage of Lyapunov–LaSalle’s invariance principle (LLIP). Last, numerical simulations are carried out in order to verify the validity of our theoretical results.http://dx.doi.org/10.1155/2021/5585175 |
| spellingShingle | A. M. Elaiw A. S. Alofi Global Dynamics of Secondary DENV Infection with Diffusion Journal of Mathematics |
| title | Global Dynamics of Secondary DENV Infection with Diffusion |
| title_full | Global Dynamics of Secondary DENV Infection with Diffusion |
| title_fullStr | Global Dynamics of Secondary DENV Infection with Diffusion |
| title_full_unstemmed | Global Dynamics of Secondary DENV Infection with Diffusion |
| title_short | Global Dynamics of Secondary DENV Infection with Diffusion |
| title_sort | global dynamics of secondary denv infection with diffusion |
| url | http://dx.doi.org/10.1155/2021/5585175 |
| work_keys_str_mv | AT amelaiw globaldynamicsofsecondarydenvinfectionwithdiffusion AT asalofi globaldynamicsofsecondarydenvinfectionwithdiffusion |