Department of Mathematical Science, University of Stellenbosch, Private Bag X1, Matieland, Stellenbosch 7602, South Africa.
Math Biosci Eng. 2013 Jun;10(3):843-60. doi: 10.3934/mbe.2013.10.843.
Substance abuse is a global menace with immeasurable consequences to the health of users, the quality of life and the economy of countries affected. Although the prominently known routes of initiation into drug use are; by contact between potential users and individuals already using the drugs and self initiation, the role played by a special class of individuals referred to as drug lords can not be ignored. We consider a simple but useful compartmental model of drug use that accounts for the contribution of contagion and drug lords to initiation into drug use and drug epidemics. We show that the model has a drug free equilibrium when the threshold parameter R0 is less that unity and a drug persistent equilibrium when R0 is greater than one. In our effort to ascertain the effect of policing in the control of drug epidemics, we include a term accounting for law enforcement. Our results indicate that increased law enforcement greatly reduces the prevalence of substance abuse. In addition, initiation resulting from presence of drugs in circulation can be as high as seven times higher that initiation due to contagion alone.
药物滥用是一种全球性的威胁，对使用者的健康、生活质量和受影响国家的经济造成了无法估量的后果。尽管众所周知的吸毒途径有：潜在使用者与已经使用毒品的个人之间的接触和自我启动，但是被称为毒枭的一类特殊个人所扮演的角色不容忽视。我们考虑了一个简单但有用的药物使用 compartmental 模型，该模型考虑了传染和毒枭对吸毒和药物流行的贡献。我们表明，当阈值参数 R0 小于 1 时，模型具有无药物平衡，当 R0 大于 1 时，模型具有药物持续平衡。为了确定执法在控制药物流行中的作用，我们引入了一个考虑执法的术语。我们的结果表明，加强执法可以大大降低药物滥用的流行率。此外，由于流通中的毒品而导致的启动可能是由于传染单独导致的启动的七倍以上。
