Stability Analysis of a Drug-Addict Epidemic Model with Education

Abstract

This article discusses the model of drug addicts with education. The analysis begins by constructing the model. Next, the equilibrium point and its stability conditions are determined, and numerical simulation is given at the end. Two equilibrium points obtained, those are the drug-addicts free equilibrium point and the drug-addicts endemic equilibrium point. Then the basic reproduction number (RO) as the expected value of infection per unit time is determined using the Next Generation Matrix approach. Based on the numerical simulation, every population is stable near to the drug-free equilibrium point at RO<1, means the population of the drug-addict constantly decrease and on a certain condition will be non-existent, and stable around to drug-endemic equilibrium point at RO>1, means the drug-addict population will constantly increase so the drug epidemic occurred. Through the numerical simulation, the biggest education is given, the more population susceptible to education increase which caused the number population of susceptible without education decrease.