Analysis of a mathematical model for interactions between \(T\) cells and macrophages (Q2786004)
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scientific article; zbMATH DE number 5786185
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Analysis of a mathematical model for interactions between \(T\) cells and macrophages |
scientific article; zbMATH DE number 5786185 |
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16 September 2010
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dynamical systems
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qualitative behaviour
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immunology
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Analysis of a mathematical model for interactions between \(T\) cells and macrophages (English)
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The aim of this article is to carry out a mathematical analysis of a system of ordinary differential equations introduced by \textit{R. Lev Bar-Or} [Math. Biosci. 163, No.~1, 35--58 (2000; Zbl 0946.92010)] 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. In the reviewer's opinion, the results of the simpler model in this paper agree with the phenomena that whether Th1 or Th2 dominates immune response depends on the infection site.
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