Behrens D A, Caulkins J P, Tragler G, Haunschmied J L, Feichtinger G
Department of Operations Research and Systems Theory, Vienna University of Technology, Austria.
Math Biosci. 1999 Jun;159(1):1-20. doi: 10.1016/s0025-5564(99)00016-4.
We set up a time-continuous version of the first-order difference equation model of cocaine use introduced by Everingham and Rydell [S.S. Everingham, C.P. Rydell, Modeling the Demand for Cocaine, MR-332-ONDCP/A/DPRC, RAND, Santa Monica, CA, 1994] and extend it by making initiation an endogenous function of prevalence. This function reflects both the epidemic spread of drug use as users 'infect' non-users and Musto's [D.F. Musto, The American Disease: Origins of Narcotic Control, Oxford University, New York, 1987] hypothesis that drug epidemics die out when a new generation is deterred from initiating drug use by observing the ill effects manifest among heavy users. Analyzing the model's dynamics suggests that drug prevention can temper drug prevalence and consumption, but that drug treatment's effectiveness depends critically on the stage in the epidemic in which it is employed. Reducing the number of heavy users in the early stages of an epidemic can be counter-productive if it masks the risks of drug use and, thereby, removes a disincentive to initiation. This strong dependence of an intervention's effectiveness on the state of the dynamic system illustrates the pitfalls of applying a static control policy in a dynamic context.
我们建立了由埃弗林厄姆和赖德尔提出的可卡因使用一阶差分方程模型的时间连续版本[S.S.埃弗林厄姆、C.P.赖德尔，《可卡因需求建模》，MR - 332 - ONDCP/A/DPRC，兰德公司，加利福尼亚州圣莫尼卡，1994年]，并通过使开始使用成为流行率的内生函数对其进行扩展。该函数既反映了吸毒的流行传播，即使用者“感染”非使用者，也反映了马斯托[D.F.马斯托，《美国疾病：麻醉品管制的起源》，牛津大学出版社，纽约，1987年]的假设，即当新一代通过观察重度使用者中显现的不良影响而被阻止开始吸毒时，毒品流行就会消退。对该模型动态的分析表明，毒品预防可以缓和毒品流行率和消费量，但毒品治疗的效果关键取决于其实施时流行所处的阶段。如果在流行早期减少重度使用者的数量掩盖了吸毒风险，从而消除了对开始吸毒的抑制因素，那么这可能会适得其反。干预效果对动态系统状态的这种强烈依赖性说明了在动态环境中应用静态控制政策的缺陷。
