Hopf bifurcation analysis of nonlinear HIV infection model and the effect of delayed immune response with drug therapies
Abstract A mathematical model of HIV infection with the combination of drug therapy including cytotoxic T-lymphocyte (CTL) and the antibody immune response is examined. The threshold value represented as the basic reproduction ratio R 0 $R_{0}$ is derived. This reveals that R 0 < 1 $R_{0} < 1$...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-08-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-020-01410-8 |
| _version_ | 1828489646792769536 |
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| author | V. Geetha S. Balamuralitharan |
| author_facet | V. Geetha S. Balamuralitharan |
| author_sort | V. Geetha |
| collection | DOAJ |
| description | Abstract A mathematical model of HIV infection with the combination of drug therapy including cytotoxic T-lymphocyte (CTL) and the antibody immune response is examined. The threshold value represented as the basic reproduction ratio R 0 $R_{0}$ is derived. This reveals that R 0 < 1 $R_{0} < 1$ is locally asymptotically stable in the viral free steady state, and the infected steady state condition remains locally asymptotically stable with R 0 > 1 $R_{0} > 1$ in the absence of a delay in the immune response. Moreover, the existence of Hopf bifurcation with CTL response delay is demonstrated. The estimation of delay length is used to maintain stability. Numerical simulations are implemented to explain the mathematical results. |
| first_indexed | 2024-12-11T10:29:39Z |
| format | Article |
| id | doaj.art-b9595bc44c9c416580546da62c193f30 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-11T10:29:39Z |
| publishDate | 2020-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-b9595bc44c9c416580546da62c193f302022-12-22T01:11:00ZengSpringerOpenBoundary Value Problems1687-27702020-08-012020111510.1186/s13661-020-01410-8Hopf bifurcation analysis of nonlinear HIV infection model and the effect of delayed immune response with drug therapiesV. Geetha0S. Balamuralitharan1Department of Mathematics, SRM Institute of Science and TechnologyDepartment of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and TechnologyAbstract A mathematical model of HIV infection with the combination of drug therapy including cytotoxic T-lymphocyte (CTL) and the antibody immune response is examined. The threshold value represented as the basic reproduction ratio R 0 $R_{0}$ is derived. This reveals that R 0 < 1 $R_{0} < 1$ is locally asymptotically stable in the viral free steady state, and the infected steady state condition remains locally asymptotically stable with R 0 > 1 $R_{0} > 1$ in the absence of a delay in the immune response. Moreover, the existence of Hopf bifurcation with CTL response delay is demonstrated. The estimation of delay length is used to maintain stability. Numerical simulations are implemented to explain the mathematical results.http://link.springer.com/article/10.1186/s13661-020-01410-8HIV Delay modelLocal StabilityHopf bifurcation |
| spellingShingle | V. Geetha S. Balamuralitharan Hopf bifurcation analysis of nonlinear HIV infection model and the effect of delayed immune response with drug therapies Boundary Value Problems HIV Delay model Local Stability Hopf bifurcation |
| title | Hopf bifurcation analysis of nonlinear HIV infection model and the effect of delayed immune response with drug therapies |
| title_full | Hopf bifurcation analysis of nonlinear HIV infection model and the effect of delayed immune response with drug therapies |
| title_fullStr | Hopf bifurcation analysis of nonlinear HIV infection model and the effect of delayed immune response with drug therapies |
| title_full_unstemmed | Hopf bifurcation analysis of nonlinear HIV infection model and the effect of delayed immune response with drug therapies |
| title_short | Hopf bifurcation analysis of nonlinear HIV infection model and the effect of delayed immune response with drug therapies |
| title_sort | hopf bifurcation analysis of nonlinear hiv infection model and the effect of delayed immune response with drug therapies |
| topic | HIV Delay model Local Stability Hopf bifurcation |
| url | http://link.springer.com/article/10.1186/s13661-020-01410-8 |
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