  We explore simple models aimed at the study of social contagion, in which
contagion proceeds through two stages. When coupled with demographic turnover,
we show that two-stage contagion leads to nonlinear phenomena which are not
present in the basic `classical' models of mathematical epidemiology. These
include: bistability, critical transitions, endogenous oscillations, and
excitability, suggesting that contagion models with stages could account for
some aspects of the complex dynamics encountered in social life. These
phenomena, and the bifurcations involved, are studied by a combination of
analytical and numerical means.
