Abstract:
This article discussed mathematical model of alcoholism with optimal control.Model is designed
using system of differential equations based on Susceptible, Infectible and Resistant (SIR) model. Infected
individuals is divided into two compartments, admitted and non-admitted to alcoholism. Optimal control is used
to prevent interaction between susceptible individual and infected individuals. Stability analysis is done locally
using Routh-Hurwitz criteria. It can be shown that optimal control determines stability of the system. In the end
of article, numerical simulation is given to illustrate uncontrolled and controlled system. The results show
optimal control succeed to reduce infected individuals. Controlled system has higher susceptible individuals and
has lower infected individuals than uncontrolled system.
