  We study the spread of disease in an SIS model. The model considered is a
time-varying, switched model, in which the parameters of the SIS model are
subject to abrupt change. We show that the joint spectral radius can be used as
a threshold parameter for this model in the spirit of the basic reproduction
number for time-invariant models. We also present conditions for persistence
and the existence of periodic orbits for the switched model and results for a
stochastic switched model.
