Stability analysis of mathematical model of drug abuse case rehabilitation program in East Java

The case of drug abuse is still a chronic problem for many countries, including Indonesia. One of the actions taken by the government in dealing with drug abuse cases is a rehabilitation program for addicts. Therefore, it is necessary to construct a mathematical model to observe the dynamics of the rehabilitation program for drug abuse cases. The mathematical model for the rehabilitation program for drug abuse cases is constructed based on the SIR epidemic model. Furthermore, through stability analysis, it was found that the model is asymptotically stable around the drug-free equilibrium point (E0) if R0 < 1 and is asymptotically stable around the drug-endemic equilibrium point (E1) if it meets the appropriate conditions obtained based on the Routh-Hurwitz criteria. The results of numerical simulations on the mathematical model of the rehabilitation program for drug abuse cases show that the more individuals who participate in the rehabilitation program, the faster the drug-free state will be obtained.