Abstract In this paper, we have developed a mathematical
model of alcohol abuse which consists of four compartments
corresponding to four population classes, namely, moderate
and occasional drinkers, heavy drinkers, drinkers in treatment
and temporarily recovered class. We have discussed about
basic properties of the system. Sensitivity analysis of the
system is also discussed. Next, Basic reproduction number
(R0) is calculated. The stability analysis of the model shows
that the system is locally asymptotically stable at disease free
equilibrium E0 when R0 < 1. When R0 > 1, endemic equilibrium
E∗ exists and the system becomes locally asymptotically
stable at E∗ and E0 becomes unstable. We have also
discussed the global stability of the system at E0. It is also
found that a backward bifurcation may occur at R0 = 1. Next
we have discussed the drinking epidemic model with treatment
control.
An objective functional is considered which is based on a combination of minimizing the number of heavy drinkers and the cost of treatment.
Then an optimal control is obtained which minimizes the objective functional.
Our numerical findings are illustrated through computer simulations using MATLAB,
which show the reliability of our model from the practical point of view.
Epidemiological implications of our analytical findings are addressed critically