Optimal Control Strategy for Alcoholism Model with Two Infected Compartments

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.