Analysis of a mathematical model for interactions between T cells and macrophages
The aim of this article is to carry out a mathematical analysis of a system of ordinary differential equations introduced by Lev Bar-Or to model the interactions between T cells and macrophages. Under certain restrictions on the parameters of the model, theorems are proved about the number of st...
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| Language: | English |
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Texas State University
2010-08-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2010/115/abstr.html |
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doaj-4ced53ab7c064baebfe419b748b0cc2c2020-11-24T21:33:13ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912010-08-012010115,110Analysis of a mathematical model for interactions between T cells and macrophagesAlan D. RendallThe aim of this article is to carry out a mathematical analysis of a system of ordinary differential equations introduced by Lev Bar-Or to model the interactions between T cells and macrophages. Under certain restrictions on the parameters of the model, theorems are proved about the number of stationary solutions and their stability. In some cases the existence of periodic solutions or heteroclinic cycles is ruled out. Evidence is presented that the same biological phenomena could be equally well described by a simpler model. http://ejde.math.txstate.edu/Volumes/2010/115/abstr.htmlDynamical systemsqualitative behaviourimmunology |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Alan D. Rendall |
| spellingShingle |
Alan D. Rendall Analysis of a mathematical model for interactions between T cells and macrophages Electronic Journal of Differential Equations Dynamical systems qualitative behaviour immunology |
| author_facet |
Alan D. Rendall |
| author_sort |
Alan D. Rendall |
| title |
Analysis of a mathematical model for interactions between T cells and macrophages |
| title_short |
Analysis of a mathematical model for interactions between T cells and macrophages |
| title_full |
Analysis of a mathematical model for interactions between T cells and macrophages |
| title_fullStr |
Analysis of a mathematical model for interactions between T cells and macrophages |
| title_full_unstemmed |
Analysis of a mathematical model for interactions between T cells and macrophages |
| title_sort |
analysis of a mathematical model for interactions between t cells and macrophages |
| publisher |
Texas State University |
| series |
Electronic Journal of Differential Equations |
| issn |
1072-6691 |
| publishDate |
2010-08-01 |
| description |
The aim of this article is to carry out a mathematical analysis of a system of ordinary differential equations introduced by Lev Bar-Or to model the interactions between T cells and macrophages. Under certain restrictions on the parameters of the model, theorems are proved about the number of stationary solutions and their stability. In some cases the existence of periodic solutions or heteroclinic cycles is ruled out. Evidence is presented that the same biological phenomena could be equally well described by a simpler model. |
| topic |
Dynamical systems qualitative behaviour immunology |
| url |
http://ejde.math.txstate.edu/Volumes/2010/115/abstr.html |
| work_keys_str_mv |
AT alandrendall analysisofamathematicalmodelforinteractionsbetweentcellsandmacrophages |
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1725954225860509696 |