An Interdisciplinary Journal

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

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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Last updated: *June 19, 2001*