Mathematical Modeling of the Dynamics of Psychoactive Drug Abuse with Intervention of Control Agencies

Drug abuse continues to pose a significant threat to both developed and developing countries. This paper examines the dynamics of psychoactive drug abuse with intervention of control agencies. The study established that the drug abuse model remains positively invariant over time, as indicated by the positivity of the solutions to the model equations. The study identified both drug abuse endemic and drug abuse free equilibrium states. Basic reproduction number was obtained using the method of next generation matrix. The local stability of the drug abuse free equilibrium state was analyzed using Jacobian method and the analysis showed that the drug abuse free equilibrium state is locally asymptotically stable since all the Eigen values are negative. Similarly, the global stability analysis of the drug abuse free equilibrium state confirmed that the system is globally asymptotically stable. The sensitivity index was computed. The results indicate that parameters with positive sensitivity indices increase the prevalence, while those with negative sensitivity indices decrease it. This suggests that these parameters have the ability to either increase or decrease the persistence of drug abuse in the population. The numerical simulation of the model was performed using MATLAB R2015a software and results show that enlightenment and law enforcement agencies play a vital role in reducing the spread of drug abuse. This research recommends intensification of early enlightenment to curtail the spread of drug abuse. Also making more policies, enactment and enforcement of more laws that will check the use of hard drugs