  In the last decades, the interest to understand the connection between brain
and body has grown notably. For example, in psychoneuroimmunology many studies
associate stress, arising from many different sources and situations, to
changes in the immune system from the medical or immunological point of view as
well as from the biochemical one. In this paper we identify important
behaviours of this interplay between the immune system and stress from medical
studies and seek to represent them qualitatively in a paradigmatic, yet simple,
mathematical model. To that end we develop a differential equation model with
two equations for infection level and immune system, which integrates the
effects of stress as an additional parameter. We are able to reproduce a stable
healthy state for little stress, an oscillatory state between healthy and
infected states for high stress, and a "burn-out" or stable sick state for
extremely high stress. The mechanism between the different dynamics is
controlled by two saddle-node in cycle (SNIC) bifurcations. Furthermore, our
model is able to capture an induced infection upon dropping from moderate to
low stress, and it predicts increasing infection periods upon increasing before
eventually reaching a burn-out state.
