Department of Mathematics, University of Stellenbosch, Matieland, South Africa.
Bull Math Biol. 2013 Jan;75(1):24-48. doi: 10.1007/s11538-012-9790-5. Epub 2012 Nov 29.
Substance abuse remains a global problem, with immense health and social consequences. Crystal meth, known as 'tik' in South Africa, is a growing problem, and its supply chains have equally grown due to increased numbers of 'tik' users, especially in the Western Cape province of South Africa. We consider a model for 'tik' use that tracks drug-supply chains, and accounts for rehabilitation and amelioration for the addicted. We analyse the model and show that it has a unique drug-free equilibrium. We prove that the drug-free equilibrium is globally stable when the reproduction number is less than one. We also consider both slow and fast dynamics, and show that there is a unique drug-persistent equilibrium when the reproduction number exceeds one. The model is fitted to data on 'tik' users in rehabilitation in the Western Cape province. A sensitivity analysis reveals that the parameters with the most control over the epidemic are the quitting rate of light-drug users and the person-to-person contact rate between susceptible individuals and 'tik' users. This suggests that programs aimed at light-drug users that encourage them to quit will be significantly more effective than targeting hard-drug users, either in quitting or in rehabilitation. Similarly, the person-to-person contact rate may be reduced by social programs that raise awareness of the dangers of 'tik' use and discourage light users from recruiting others.
药物滥用仍然是一个全球性问题，对健康和社会造成了巨大影响。冰毒，在南非被称为“Tik”，是一个日益严重的问题，由于越来越多的“Tik”使用者，特别是在南非西开普省，其供应链也同样增长。我们考虑了一个追踪毒品供应链的“Tik”使用模型，并考虑了成瘾者的康复和改善。我们分析了该模型，发现当繁殖数小于 1 时，它有一个独特的无毒品平衡。我们证明当繁殖数小于 1 时，无毒品平衡是全局稳定的。我们还考虑了慢和快动态，并发现当繁殖数大于 1 时，存在一个独特的药物持续平衡。该模型适用于西开普省康复中心的“Tik”使用者数据。敏感性分析表明，对流行病控制最有影响的参数是轻度药物使用者的戒烟率和易感人群与“Tik”使用者之间的人际接触率。这表明，旨在鼓励轻度药物使用者戒烟的项目将比针对硬毒品使用者的项目更有效，无论是在戒烟还是康复方面。同样，通过提高对“Tik”使用危险的认识并劝阻轻度使用者招募他人的社会项目，人际接触率可能会降低。
