This paper proposes a mathematical compartmental model that describes the dynamics of drug misuse among Nigerians. The model was formulated based on view, ideology, and perspective and used a compartmental model to analyse and comprehend the growth of drug abuse among addicts, individuals, and the general community, as well as ex-addicts and addicts. Hospitalisation is included as an intervention in general. The basic reproduction number \((R_0)\) is calculated and found to be less than one, indicating that the spread of drug abuse in the population is under control and could be easily eliminated if hospital treatment is seriously abated. The effective reproduction number \((R_e)\) is also calculated and found to be less than one, indicating that the spread of drug abuse in the population will not persist with hospital treatment as an intervention. Berkeley Madonna modelling software was used to compute numerical simulations and visualisations of the interactions between diverse groups of people, which are represented by a series of differential equations, in order to see the spread of drug misuse dynamics and the effect of the interventions. The finding shows that the rapid way to reduce the drug abuse is sending the hospitalised citizens to addicted citizens in order to give testimony and scare them in order to allow the addicted to go to the hospital by themselves without persuading them.