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AKB: Biologische Physik

AKB 30: Poster Session I

AKB 30.33: Poster

Montag, 27. März 2006, 15:30–18:00, P1

Th1–Th2 Regulation and Allergy: Bifurcation Analysis of a Stroboscopic Map — •Reinhard Vogel and Ulrich Behn — Institut für Theoretische Physik, Universität Leipzig, POB 100 920, 04009 Leipzig

A previously proposed mathematical model [1] 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 closer 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 present a bifurcation analysis of the non-autonomous 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. We further discuss the dependence of the fixed point manifolds on the dose of the allergen injections and on small variations of the cytokine background.

[1] J. Richter, G. Metzner, U. Behn, Venom immunotherapy: A mathematical model, J. Theor. Med. 4, 119–132 (2002)