A delay-differential equation model of HIV related cancer--immune system dynamics
In the human body, the appearance of tumor cells usually turns on the defensive immune mechanisms. It is therefore of great importance to understand links between HIV related immunosuppression and cancer prognosis. In the paper we present a simple model of HIV related cancer - immune system interact...
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| Format: | Article |
| Language: | English |
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AIMS Press
2011-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.627 |
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| _version_ | 1832590178184593408 |
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| author | Urszula Foryś Jan Poleszczuk |
| author_facet | Urszula Foryś Jan Poleszczuk |
| author_sort | Urszula Foryś |
| collection | DOAJ |
| description | In the human body, the appearance of tumor cells usually turns on the defensive immune mechanisms. It is therefore of great importance to understand links between HIV related immunosuppression and cancer prognosis. In the paper we present a simple model of HIV related cancer - immune system interactions in vivo which takes into account a delay describing the time needed by CD$4^+$ T lymphocyte to regenerate after eliminating a cancer cell. The model assumes also the linear response of immune system to tumor presence.We perform a mathematical analysis of the steady states stability and discuss the biological meanings of these steady states. Numerical simulations are also presented to illustrate the predictions of the model. |
| format | Article |
| id | doaj-art-386d8b47b95a4e51b2a03d3829f45bb3 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-386d8b47b95a4e51b2a03d3829f45bb32025-01-24T02:01:39ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-03-018262764110.3934/mbe.2011.8.627A delay-differential equation model of HIV related cancer--immune system dynamicsUrszula Foryś0Jan Poleszczuk1University of Warsaw, Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, Banacha 2, 02-097 WarsawUniversity of Warsaw, Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, Banacha 2, 02-097 WarsawIn the human body, the appearance of tumor cells usually turns on the defensive immune mechanisms. It is therefore of great importance to understand links between HIV related immunosuppression and cancer prognosis. In the paper we present a simple model of HIV related cancer - immune system interactions in vivo which takes into account a delay describing the time needed by CD$4^+$ T lymphocyte to regenerate after eliminating a cancer cell. The model assumes also the linear response of immune system to tumor presence.We perform a mathematical analysis of the steady states stability and discuss the biological meanings of these steady states. Numerical simulations are also presented to illustrate the predictions of the model.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.627cancertime delayaidsstability switches.hiv infection |
| spellingShingle | Urszula Foryś Jan Poleszczuk A delay-differential equation model of HIV related cancer--immune system dynamics Mathematical Biosciences and Engineering cancer time delay aids stability switches. hiv infection |
| title | A delay-differential equation model of HIV related cancer--immune system dynamics |
| title_full | A delay-differential equation model of HIV related cancer--immune system dynamics |
| title_fullStr | A delay-differential equation model of HIV related cancer--immune system dynamics |
| title_full_unstemmed | A delay-differential equation model of HIV related cancer--immune system dynamics |
| title_short | A delay-differential equation model of HIV related cancer--immune system dynamics |
| title_sort | delay differential equation model of hiv related cancer immune system dynamics |
| topic | cancer time delay aids stability switches. hiv infection |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.627 |
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