Global Properties of a Diffusive SARS-CoV-2 Infection Model with Antibody and Cytotoxic T-Lymphocyte Immune Responses
A severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection can lead to morbidity and mortality. SARS-CoV-2 infects the epithelial cells of the respiratory tract and causes coronavirus disease 2019 (COVID-19). The immune system’s response plays a significant role in viral progression. T...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/1/190 |
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| author | Ahmed. M. Elaiw Abdullah J. Alsaedi Aatef. D. Hobiny Shaban. A. Aly |
| author_facet | Ahmed. M. Elaiw Abdullah J. Alsaedi Aatef. D. Hobiny Shaban. A. Aly |
| author_sort | Ahmed. M. Elaiw |
| collection | DOAJ |
| description | A severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection can lead to morbidity and mortality. SARS-CoV-2 infects the epithelial cells of the respiratory tract and causes coronavirus disease 2019 (COVID-19). The immune system’s response plays a significant role in viral progression. This article develops and analyzes a system of partial differential equations (PDEs), which describe the in-host dynamics of SARS-CoV-2 under the effect of cytotoxic T-lymphocyte (CTL) and antibody immune responses. The model characterizes the interplay between six compartments, healthy epithelial cells (ECs), latent infected ECs, active infected ECs, free SARS-CoV-2 particles, CTLs, and antibodies. We consider the logistic growth of healthy ECs. We first investigate the properties of the model’s solutions, then, we calculate all steady states and determine the conditions of their existence and global stability. The global asymptotic stability is examined by constructing Lyapunov functions. The analytical findings are supported via numerical simulations. |
| first_indexed | 2024-03-09T09:45:19Z |
| format | Article |
| id | doaj.art-e1f0c3de4ad648bab35860b13be3b4f0 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T09:45:19Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e1f0c3de4ad648bab35860b13be3b4f02023-12-02T00:39:03ZengMDPI AGMathematics2227-73902022-12-0111119010.3390/math11010190Global Properties of a Diffusive SARS-CoV-2 Infection Model with Antibody and Cytotoxic T-Lymphocyte Immune ResponsesAhmed. M. Elaiw0Abdullah J. Alsaedi1Aatef. D. Hobiny2Shaban. A. Aly3Department 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 ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut 71516, EgyptA severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection can lead to morbidity and mortality. SARS-CoV-2 infects the epithelial cells of the respiratory tract and causes coronavirus disease 2019 (COVID-19). The immune system’s response plays a significant role in viral progression. This article develops and analyzes a system of partial differential equations (PDEs), which describe the in-host dynamics of SARS-CoV-2 under the effect of cytotoxic T-lymphocyte (CTL) and antibody immune responses. The model characterizes the interplay between six compartments, healthy epithelial cells (ECs), latent infected ECs, active infected ECs, free SARS-CoV-2 particles, CTLs, and antibodies. We consider the logistic growth of healthy ECs. We first investigate the properties of the model’s solutions, then, we calculate all steady states and determine the conditions of their existence and global stability. The global asymptotic stability is examined by constructing Lyapunov functions. The analytical findings are supported via numerical simulations.https://www.mdpi.com/2227-7390/11/1/190SARS-CoV-2COVID-19immune responsereaction–diffusion virus infection modelglobal asymptotic stabilityLyapunov functions |
| spellingShingle | Ahmed. M. Elaiw Abdullah J. Alsaedi Aatef. D. Hobiny Shaban. A. Aly Global Properties of a Diffusive SARS-CoV-2 Infection Model with Antibody and Cytotoxic T-Lymphocyte Immune Responses Mathematics SARS-CoV-2 COVID-19 immune response reaction–diffusion virus infection model global asymptotic stability Lyapunov functions |
| title | Global Properties of a Diffusive SARS-CoV-2 Infection Model with Antibody and Cytotoxic T-Lymphocyte Immune Responses |
| title_full | Global Properties of a Diffusive SARS-CoV-2 Infection Model with Antibody and Cytotoxic T-Lymphocyte Immune Responses |
| title_fullStr | Global Properties of a Diffusive SARS-CoV-2 Infection Model with Antibody and Cytotoxic T-Lymphocyte Immune Responses |
| title_full_unstemmed | Global Properties of a Diffusive SARS-CoV-2 Infection Model with Antibody and Cytotoxic T-Lymphocyte Immune Responses |
| title_short | Global Properties of a Diffusive SARS-CoV-2 Infection Model with Antibody and Cytotoxic T-Lymphocyte Immune Responses |
| title_sort | global properties of a diffusive sars cov 2 infection model with antibody and cytotoxic t lymphocyte immune responses |
| topic | SARS-CoV-2 COVID-19 immune response reaction–diffusion virus infection model global asymptotic stability Lyapunov functions |
| url | https://www.mdpi.com/2227-7390/11/1/190 |
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