  We constructed a Susceptible-Addicted-Reformed model and explored the
dynamics of nonlinear relapse in the Reformed population. The transition from
susceptible considered {\it at-risk} is modeled using a strictly decreasing
general function, mimicking an influential factor that reduces the flow into
the addicted class. The {\it basic reproductive number} is computed.
Furthermore, $R_0$ determines the local asymptotically stability of the
addicted-free equilibrium. Conditions for a forward-backward bifurcation were
established using $R_0$ and other threshold quantities. A stochastic version of
the model is presented, and some numerical examples are shown. Results showed
that the influence of the temporarily reformed individuals is highly sensitive
to the initial addicted population.
