MODEL MATEMATIKA PENYEBARAN PENGGUNA NARKOBA DENGAN ADANYA FAKTOR EDUKASI DI SUMATERA UTARA

Abstract

Drug abuse is using drugs without a doctor's instructions or prescription. Drug abuse is one of Indonesia's health and social problems, not least in the province of North Sumatra. North Sumatra Province currently has the highest number of drug abuse cases. This makes the researchers make a mathematical model of the distribution of drug users with educational factors with the SIRS epidemic model method. The first step is to modify the model, after which the equilibrium and stability points are calculated. The final step is to perform a numerical simulation on the basic reproduction number using the next-generation matrix approach. From the analysis results obtained two equilibrium points, namely the equilibrium point free of drug users and the endemic equilibrium point for drug users, but only one equilibrium point was analyzed. . Based on the numerical simulation, every population are stable near to the drug free equilibrium point at  , means the population of the drug addigt constantly decrease and on a certain condition will be non existent, and stable around to drug endemic equilbrium point at  , means the drug addict population will constantly increase so the drug epidemic occurred. From the simulation, it is found that the greater the rate of education, the more the number of vulnerable population with education will increase and the number of vulnerable population without education will decrease