Stability of a discrete-time general delayed viral model with antibody and cell-mediated immune responses
Abstract We propose a discrete-time viral model with antibody and cell-mediated immune responses. Two types of infected cells are incorporated into the model, namely latently infected and actively infected. The incidence rate of infection as well as the production and removal rates of all compartmen...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-02-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-020-2526-1 |
| _version_ | 1818623195663564800 |
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| author | A. M. Elaiw M. A. Alshaikh |
| author_facet | A. M. Elaiw M. A. Alshaikh |
| author_sort | A. M. Elaiw |
| collection | DOAJ |
| description | Abstract We propose a discrete-time viral model with antibody and cell-mediated immune responses. Two types of infected cells are incorporated into the model, namely latently infected and actively infected. The incidence rate of infection as well as the production and removal rates of all compartments are modeled by general nonlinear functions. The model contains three types of intracellular time delays. We utilize nonstandard finite difference (NSFD) method to discretize the continuous-time model. We prove that NSFD preserves the positivity and boundedness of the solutions of the model. Based on four threshold parameters, the existence of the five equilibria of the model is established. We perform global stability of all equilibria of the model by using Lyapunov approach. Numerical simulations are carried out to illustrate our theoretical results. The impact of time delay on the viral dynamics is established. |
| first_indexed | 2024-12-16T18:37:12Z |
| format | Article |
| id | doaj.art-4dc8a704d2214be6866a928f724c0764 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-16T18:37:12Z |
| publishDate | 2020-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-4dc8a704d2214be6866a928f724c07642022-12-21T22:21:08ZengSpringerOpenAdvances in Difference Equations1687-18472020-02-012020115110.1186/s13662-020-2526-1Stability of a discrete-time general delayed viral model with antibody and cell-mediated immune responsesA. M. Elaiw0M. A. Alshaikh1Department of Mathematics, Faculty of Science, King Abdulaziz UniversityDepartment of Mathematics, Faculty of Science, King Abdulaziz UniversityAbstract We propose a discrete-time viral model with antibody and cell-mediated immune responses. Two types of infected cells are incorporated into the model, namely latently infected and actively infected. The incidence rate of infection as well as the production and removal rates of all compartments are modeled by general nonlinear functions. The model contains three types of intracellular time delays. We utilize nonstandard finite difference (NSFD) method to discretize the continuous-time model. We prove that NSFD preserves the positivity and boundedness of the solutions of the model. Based on four threshold parameters, the existence of the five equilibria of the model is established. We perform global stability of all equilibria of the model by using Lyapunov approach. Numerical simulations are carried out to illustrate our theoretical results. The impact of time delay on the viral dynamics is established.https://doi.org/10.1186/s13662-020-2526-1Viral dynamicsLatencyTime delayGlobal stabilityAntibodyCell-mediated response |
| spellingShingle | A. M. Elaiw M. A. Alshaikh Stability of a discrete-time general delayed viral model with antibody and cell-mediated immune responses Advances in Difference Equations Viral dynamics Latency Time delay Global stability Antibody Cell-mediated response |
| title | Stability of a discrete-time general delayed viral model with antibody and cell-mediated immune responses |
| title_full | Stability of a discrete-time general delayed viral model with antibody and cell-mediated immune responses |
| title_fullStr | Stability of a discrete-time general delayed viral model with antibody and cell-mediated immune responses |
| title_full_unstemmed | Stability of a discrete-time general delayed viral model with antibody and cell-mediated immune responses |
| title_short | Stability of a discrete-time general delayed viral model with antibody and cell-mediated immune responses |
| title_sort | stability of a discrete time general delayed viral model with antibody and cell mediated immune responses |
| topic | Viral dynamics Latency Time delay Global stability Antibody Cell-mediated response |
| url | https://doi.org/10.1186/s13662-020-2526-1 |
| work_keys_str_mv | AT amelaiw stabilityofadiscretetimegeneraldelayedviralmodelwithantibodyandcellmediatedimmuneresponses AT maalshaikh stabilityofadiscretetimegeneraldelayedviralmodelwithantibodyandcellmediatedimmuneresponses |