Ackleh Azmy S, Fitzpatrick Ben G, Scribner Richard, Simonsen Neal, Thibodeaux Jeremy J
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504.
Math Comput Model. 2009 Aug 1;50(3-4):481-497. doi: 10.1016/j.mcm.2009.03.012.
Recently we developed a model composed of five impulsive differential equations that describes the changes in drinking patterns (that persist at epidemic level) amongst college students. Many of the model parameters cannot be measured directly from data; thus, an inverse problem approach, which chooses the set of parameters that results in the "best" model to data fit, is crucial for using this model as a predictive tool. The purpose of this paper is to present the procedure and results of an unconventional approach to parameter estimation that we developed after more common approaches were unsuccessful for our specific problem. The results show that our model provides a good fit to survey data for 32 campuses. Using these parameter estimates, we examined the effect of two hypothetical intervention policies: 1) reducing environmental wetness, and 2) penalizing students who are caught drinking. The results suggest that reducing campus wetness may be a very effective way of reducing heavy episodic (binge) drinking on a college campus, while a policy that penalizes students who drink is not nearly as effective.
最近，我们开发了一个由五个脉冲微分方程组成的模型，该模型描述了大学生中（在流行水平持续存在的）饮酒模式的变化。许多模型参数无法直接从数据中测量；因此，反问题方法，即选择能使模型与数据达到“最佳”拟合的参数集，对于将该模型用作预测工具至关重要。本文的目的是介绍我们在更常见的方法对我们的特定问题不成功之后开发的一种非常规参数估计方法的过程和结果。结果表明，我们的模型与32个校园的调查数据拟合良好。利用这些参数估计值，我们研究了两种假设干预政策的效果：1）降低环境湿度，2）惩罚被抓到饮酒的学生。结果表明，降低校园湿度可能是减少大学校园重度间歇性（狂饮）饮酒的非常有效的方法，而惩罚饮酒学生的政策效果则远不如前者。
