Modeling Cancer in HIV-1 Infected Individuals: Equilibria, Cycles and Chaotic Behavior
For HIV-infected individuals, cancer remains a significant burden. Gaining insight into the epidemiology and mechanisms that underlieAIDS-related cancers can provide us with a better understanding of cancer immunity and viral oncogenesis. In this paper, an HIV-1 dynamicalmodel incorporating the AIDS...
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AIMS Press
2006-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.313 |
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| author | Jie Lou Tommaso Ruggeri Claudio Tebaldi |
| author_facet | Jie Lou Tommaso Ruggeri Claudio Tebaldi |
| author_sort | Jie Lou |
| collection | DOAJ |
| description | For HIV-infected individuals, cancer remains a significant burden. Gaining insight into the epidemiology and mechanisms that underlieAIDS-related cancers can provide us with a better understanding of cancer immunity and viral oncogenesis. In this paper, an HIV-1 dynamicalmodel incorporating the AIDS-related cancer cells was studied. The model consists of three components, cancer cells, healthy CD4+ T lymphocytesand infected CD4+ T lymphocytes, and can have six steady states. We discuss the existence, the stability properties and the biological meaningsof these steady states, in particular for the positive one: cancer-HIV-healthy cells steady state. We find conditions for Hopf bifurcation ofthe positive steady state, leading to periodic solutions, sequences of period doubling bifurcations and appearance of chaos. Further, chaos andperiodic behavior alternate. Our results are consistent with some clinical and experimental observations. |
| format | Article |
| id | doaj-art-2fcb7c74867a462bbd722fbe98e655fc |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-2fcb7c74867a462bbd722fbe98e655fc2025-01-24T01:51:19ZengAIMS PressMathematical Biosciences and Engineering1551-00182006-01-013231332410.3934/mbe.2006.3.313Modeling Cancer in HIV-1 Infected Individuals: Equilibria, Cycles and Chaotic BehaviorJie Lou0Tommaso Ruggeri1Claudio Tebaldi2Department of Mathematics, Shanghai University, 99 Shangda Road Shanghai 200444, P. R.Department of Mathematics, Shanghai University, 99 Shangda Road Shanghai 200444, P. R.Department of Mathematics, Shanghai University, 99 Shangda Road Shanghai 200444, P. R.For HIV-infected individuals, cancer remains a significant burden. Gaining insight into the epidemiology and mechanisms that underlieAIDS-related cancers can provide us with a better understanding of cancer immunity and viral oncogenesis. In this paper, an HIV-1 dynamicalmodel incorporating the AIDS-related cancer cells was studied. The model consists of three components, cancer cells, healthy CD4+ T lymphocytesand infected CD4+ T lymphocytes, and can have six steady states. We discuss the existence, the stability properties and the biological meaningsof these steady states, in particular for the positive one: cancer-HIV-healthy cells steady state. We find conditions for Hopf bifurcation ofthe positive steady state, leading to periodic solutions, sequences of period doubling bifurcations and appearance of chaos. Further, chaos andperiodic behavior alternate. Our results are consistent with some clinical and experimental observations.https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.313chaos.hiv-1 infectionhopf bifurcationstabilitysteady statecancer |
| spellingShingle | Jie Lou Tommaso Ruggeri Claudio Tebaldi Modeling Cancer in HIV-1 Infected Individuals: Equilibria, Cycles and Chaotic Behavior Mathematical Biosciences and Engineering chaos. hiv-1 infection hopf bifurcation stability steady state cancer |
| title | Modeling Cancer in HIV-1 Infected Individuals: Equilibria, Cycles and Chaotic Behavior |
| title_full | Modeling Cancer in HIV-1 Infected Individuals: Equilibria, Cycles and Chaotic Behavior |
| title_fullStr | Modeling Cancer in HIV-1 Infected Individuals: Equilibria, Cycles and Chaotic Behavior |
| title_full_unstemmed | Modeling Cancer in HIV-1 Infected Individuals: Equilibria, Cycles and Chaotic Behavior |
| title_short | Modeling Cancer in HIV-1 Infected Individuals: Equilibria, Cycles and Chaotic Behavior |
| title_sort | modeling cancer in hiv 1 infected individuals equilibria cycles and chaotic behavior |
| topic | chaos. hiv-1 infection hopf bifurcation stability steady state cancer |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.313 |
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