Summary
A previously proposed mathematical model based on a simplified scheme of Th1– Th2 regulation mediated by the cytokine network which describes the population dynamics of allergen-specific naive T cells, Th1 and Th2 cells, autocrine and cross-suppressive cytokines, and allergen is more closely investigated. The model provides a theoretical explanation of the switch from a Th2-dominated response to a Th1-dominated response to allergen in allergic individuals as a result of a hyposensitization therapy. We focus here on the bifurcation analysis of the nonautonomous dynamical system driven by periodic allergen injections. The stability of the fixed points of a stroboscopic map is investigated. The set of unstable fixed points forms the dynamical separatrix between the regions of Th2-dominated response and Th1-dominated response which is crossed during a successful therapy. The maintenance phase of the therapy holds the system near the stable fixed point of the stroboscobic map.
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Vogel, R., Behn, U. (2008). Th1–Th2 Regulation and Allergy: Bifurcation Analysis of the Non-Autonomous System. In: Deutsch, A., et al. Mathematical Modeling of Biological Systems, Volume II. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4556-4_13
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DOI: https://doi.org/10.1007/978-0-8176-4556-4_13
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