The dynamics of prisoner population model in Indonesia with a rehabilitation regulation for drug users to overcome prison overcapacity issue

This paper discusses about a mathematical model of the prisoner population with a new regulation regarding punishments to the drug users in an effort to overcome the prison overcapacity issue in Indonesia. This new regulation is launched by the Indonesia government after a fact about overcapacity of prison in Indonesia is revealed through a fire incident in a prison on 8 September 2021 that causes 41 people died and a number of people were injured. Besides, prisons in Indonesia are mostly occupied by the drug user. The model is constructed by using a compartmental model approach. The stability analysis of the equilibrium points is carried out along with its existence conditions. The analytical studies are equipped by calculate the basic reproduction number. Furthermore, this study is also equipped by numerical simulations with some scenarios. The results of this study confirm that the effect of the new regulation is able to reduce overcrowded issue in prisons in Indonesia. However, if it compare to recent prison capacity, this new regulation has not been able to suppress the number of prisoner below to its capacity limit in the short time so that it is needed to consider other solutions as the additional regulation and polic