The Development of White-Comiskey Model on Drug Users Dynamics

Abstract

This thesis aims to discuss and analyze mathematical models of the spread of drug users based on the model of White and Comiskey (2007). In this model, population is divided into three classes, namely susceptibles, drug users, and drug users undergoing treatment. The model has three equilibrium points, i.e. one drug free and two endemic points. The stability of those points are determined according to the eigenvalues of the Jacobian matrices. The existence of the drug users are then controlled by a basic reproduction number. If the basic reproduction number is less than one, then the number of drug users will gradually decrease and disappear from the population. On the other hand, if the basic reproduction number is greater than one, then the number of drug users will gradually increase so that a number of drug users will stay in the population. In this thesis, the dynamical analysis of interaction between drug users and susceptible and the simulation was performed by varying the probability of becoming a drug user (β1) and the portion of drug users who enter treatment (ρ). In the former case, decreasing of β1 can be undertaken by government through law enforcement, no-drug campaign, etc. While in the later case, increasing of ρ can be done by improving government, family, and society initiative for saving drug users.