Nonlinear Phenomena in Complex Systems, 2000, Vol.3, No.4, pp.380--388

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2000, Volume 3, Number 4, pp.380--388

Variations of the Stability Due to the Time-Delay in the Immune Response.
N. Buric and N. Vasovic

A phenomenological model of the immune response, given by two differential equations with time-delay, is analyzed. The model has very simple formulation in terms of only two relevant quantities and a small number of independent parameters. However, the time-delay introduces the possibility of a quite complex dynamics, with various types of attractors, depending on the values of the parameters and the time-delay. In particular, we analyzed the conditions on the parameters such that a destabilizing Hopf bifurcation of the fixed points due to variations of the time-delay is possible. Chaotic solutions of the model are briefly described. We argue that the delay-differential equations are very natural mathematical framework for phenomenological models of the immune response.
Key words: immune response, delay-differential equations, stability

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