where 1 is the contact rate between potential smokers and occasional
smokers, 2 is the contact rate between occasional smokers and heavy smokers.
We assume that the class of potential smokers is increased by the recruit-
ment of individuals at a rate : In system (2), the total population is supposed
constant and P(t); L(t); S(t);Qt(t),Qp(t) are respectively the proportions of
potential smokers, occasional smokers, heavy smokers, temporarily quitters
and permanent quitters at time t. Then P(t)+L(t)+S(t)+Qt(t) +Qp(t) = 1.
Since the variable Qp of system (2) does not appear in the
rst three equations,
we will only consider the subsystem: