Modelling In Vivo HIV Dynamics under Combined Antiretroviral Treatment
In this paper a within host mathematical model for Human Immunodeficiency Virus (HIV) transmission incorporating treatment is formulated. The model takes into account the efficacy of combined antiretroviral treatment on viral growth and T cell population in the human blood. The existence of an infec...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2018/8276317 |
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| author | B. Mobisa G. O. Lawi J. K. Nthiiri |
| author_facet | B. Mobisa G. O. Lawi J. K. Nthiiri |
| author_sort | B. Mobisa |
| collection | DOAJ |
| description | In this paper a within host mathematical model for Human Immunodeficiency Virus (HIV) transmission incorporating treatment is formulated. The model takes into account the efficacy of combined antiretroviral treatment on viral growth and T cell population in the human blood. The existence of an infection free and positive endemic equilibrium is established. The basic reproduction number R0 is derived using the method of next generation matrix. We perform local and global stability analysis of the equilibria points and show that if R0<1, then the infection free equilibrium is globally asymptotically stable and theoretically the virus is cleared and the disease dies out and if R0>1, then the endemic equilibrium is globally asymptotically stable implying that the virus persists within the host. Numerical simulations are carried out to investigate the effect of treatment on the within host infection dynamics. |
| format | Article |
| id | doaj-art-9b7b859e7de94ebfb4c13a67adcd1c2b |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9b7b859e7de94ebfb4c13a67adcd1c2b2025-02-03T07:25:15ZengWileyJournal of Applied Mathematics1110-757X1687-00422018-01-01201810.1155/2018/82763178276317Modelling In Vivo HIV Dynamics under Combined Antiretroviral TreatmentB. Mobisa0G. O. Lawi1J. K. Nthiiri2Department of Mathematics, Laikipia University, P.O. Box 1100-20300, Nyahururu, KenyaDepartment of Mathematics, Masinde Muliro University of Science and Technology, P.O. Box 190-50100, Kakamega, KenyaDepartment of Mathematics, Masinde Muliro University of Science and Technology, P.O. Box 190-50100, Kakamega, KenyaIn this paper a within host mathematical model for Human Immunodeficiency Virus (HIV) transmission incorporating treatment is formulated. The model takes into account the efficacy of combined antiretroviral treatment on viral growth and T cell population in the human blood. The existence of an infection free and positive endemic equilibrium is established. The basic reproduction number R0 is derived using the method of next generation matrix. We perform local and global stability analysis of the equilibria points and show that if R0<1, then the infection free equilibrium is globally asymptotically stable and theoretically the virus is cleared and the disease dies out and if R0>1, then the endemic equilibrium is globally asymptotically stable implying that the virus persists within the host. Numerical simulations are carried out to investigate the effect of treatment on the within host infection dynamics.http://dx.doi.org/10.1155/2018/8276317 |
| spellingShingle | B. Mobisa G. O. Lawi J. K. Nthiiri Modelling In Vivo HIV Dynamics under Combined Antiretroviral Treatment Journal of Applied Mathematics |
| title | Modelling In Vivo HIV Dynamics under Combined Antiretroviral Treatment |
| title_full | Modelling In Vivo HIV Dynamics under Combined Antiretroviral Treatment |
| title_fullStr | Modelling In Vivo HIV Dynamics under Combined Antiretroviral Treatment |
| title_full_unstemmed | Modelling In Vivo HIV Dynamics under Combined Antiretroviral Treatment |
| title_short | Modelling In Vivo HIV Dynamics under Combined Antiretroviral Treatment |
| title_sort | modelling in vivo hiv dynamics under combined antiretroviral treatment |
| url | http://dx.doi.org/10.1155/2018/8276317 |
| work_keys_str_mv | AT bmobisa modellinginvivohivdynamicsundercombinedantiretroviraltreatment AT golawi modellinginvivohivdynamicsundercombinedantiretroviraltreatment AT jknthiiri modellinginvivohivdynamicsundercombinedantiretroviraltreatment |