The aim of the present study is to consider a heroin epidemic model with age-structure only in the active heroin users. The model was formulated with the help of available literature on heroin epidemic. Instead of treatment as a class, we incorporated recovered population and considered treatment as a control variable and thus a control problem is presented for further analysis. The techniques of weak derivatives and sensitivities were used for obtaining the adjoint equations. The maximum principle of Pontryagin’ type was used for obtaining the optimal value of the control variable. Sample simulations are presented at the end of the study in order to show the effectiveness of the treatment.

本研究的目的是考虑仅在活跃的海洛因使用者中具有年龄结构的海洛因流行模型。该模型是在有关海洛因流行的现有文献的帮助下制定的。我们没有将治疗视为一类，而是纳入了恢复的种群并将治疗视为控制变量，因此提出了控制问题以供进一步分析。使用微分导数和灵敏度技术来获得伴随方程。使用庞特里亚金类型的最大原理来获得控制变量的最佳值。在研究结束时提供了样本模拟，以显示治疗的有效性。