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Modeling the cytokine networkin vitro and in vivo. (English) Zbl 1107.92024
Summary: The present paper consist of two parts: in the first part an experiment investigating the endothelial cell/interleukin 1 system is analyzed by means of a model. The most interesting outcome is a bistability of the system: a small challenge will not lead to a reaction, while a challenge slightly above a certain threshold leads to a complete activation of the endothelial cells. This finding is used in the second part of the paper, where a caricature model of the innate immune response (the part of the immune system that is not based on acquired immunity) is described and analyzed. In this analysis, especially, the possible patterns of the dynamics in the absence of a challenge have been targeted.
We find a variety of behaviors possible for the resulting planar system. For certain parameter values, a small challenge is ignored, while a challenge above a certain threshold leads to a massive strike of the immune system that comes eventually to rest again. Also bistability, periodic behavior or an unstable resting state can be found. It is heuristically possible to link most of these dynamical patterns with natural or pathological situations that can be found in clinical pictures.

MSC:
92C50 Medical applications (general)
92C30 Physiology (general)
34C23 Bifurcation theory for ordinary differential equations
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