  The interplay between disease spreading and personal risk perception is of
key importance for modelling the spread of infectious diseases. We propose a
planar system of ordinary differential equations (ODEs) to describe the
co-evolution of a spreading phenomenon and the average link density in the
personal contact network. Contrary to standard epidemic models,we assume that
the contact network changes based on the current prevalence of the disease in
the population, i.e.\ it adapts to the current state of the epidemic. We assume
that personal risk perception is described using two functional responses: one
for link-breaking and one for link-creation. The focus is on applying the model
to epidemics, but we highlight other possible fields of application. We derive
an explicit form for the basic reproduction number and guarantee the existence
of at least one endemic equilibrium, for all possible functional responses.
Moreover, we show that for all functional responses, limit cycles do not exist.
