Predicting cocaine consumption in Spain: A mathematical modelling approach

This is an author's accepted manuscript of an article published in “Drugs: Education, Prevention, and Policy "; Volume 18, Issue 2, 2011; copyright Taylor & Francis; available online at: http://dx.doi.org/10.3109/09687630903443299In this article, we analyse the evolution of cocaine consumption in Spain and we predict consumption trends over the next few years. Additionally, we simulate some scenarios which aim to reduce cocaine consumption in the future (sensitivity analysis). Assuming cocaine dependency is a socially transmitted epidemic disease, this leads us to propose an epidemiological-type mathematical model to study consumption evolution. Model sensitivity analysis allows us to design strategies and analyse their effects on cocaine consumption. The model predicts that 3.5% of the Spanish population will be habitual cocaine consumers by 2015. The simulations carried out suggest that cocaine consumption prevention strategies are the best policy to reduce the habitual consumer population. In this article, we show that epidemiological-type mathematical models can be a useful tool in the analysis of the repercussion of health policy proposals in the short-time future. © 2011 Informa UK Ltd.Sánchez, E.; Villanueva Micó, RJ.; Santonja, FJ.; Rubio, M. (2011). Predicting cocaine consumption in Spain: A mathematical modelling approach. Drugs: Education, Prevention, and Policy. 18(2):108-115. doi:10.3109/09687630903443299S108115182Blower, S. M., & Dowlatabadi, H. (1994). Sensitivity and Uncertainty Analysis of Complex Models of Disease Transmission: An HIV Model, as an Example. International Statistical Review / Revue Internationale de Statistique, 62(2), 229. doi:10.2307/1403510Dutra, L., Stathopoulou, G., Basden, S. L., Leyro, T. M., Powers, M. B., & Otto, M. W. (2008). A Meta-Analytic Review of Psychosocial Interventions for Substance Use Disorders. American Journal of Psychiatry, 165(2), 179-187. doi:10.1176/appi.ajp.2007.06111851Gorman, D. M., Mezic, J., Mezic, I., & Gruenewald, P. J. (2006). Agent-Based Modeling of Drinking Behavior: A Preliminary Model and Potential Applications to Theory and Practice. American Journal of Public Health, 96(11), 2055-2060. doi:10.2105/ajph.2005.063289Jódar, L., Santonja, F. J., & González-Parra, G. (2008). Modeling dynamics of infant obesity in the region of Valencia, Spain. Computers & Mathematics with Applications, 56(3), 679-689. doi:10.1016/j.camwa.2008.01.011JOHNSON, B., ROACHE, J., AITDAOUD, N., JAVORS, M., HARRISON, J., ELKASHEF, A., … BLOCH, D. (2006). A preliminary randomized, double-blind, placebo-controlled study of the safety and efficacy of ondansetron in the treatment of cocaine dependence. Drug and Alcohol Dependence, 84(3), 256-263. doi:10.1016/j.drugalcdep.2006.02.011Levin, F. R., Evans, S. M., Brooks, D. J., & Garawi, F. (2007). Treatment of cocaine dependent treatment seekers with adult ADHD: Double-blind comparison of methylphenidate and placebo. Drug and Alcohol Dependence, 87(1), 20-29. doi:10.1016/j.drugalcdep.2006.07.004Marino, S., Hogue, I. B., Ray, C. J., & Kirschner, D. E. (2008). A methodology for performing global uncertainty and sensitivity analysis in systems biology. Journal of Theoretical Biology, 254(1), 178-196. doi:10.1016/j.jtbi.2008.04.011Martcheva, M., & Castillo-Chavez, C. (2003). Diseases with chronic stage in a population with varying size. Mathematical Biosciences, 182(1), 1-25. doi:10.1016/s0025-5564(02)00184-0Nelder, J. A., & Mead, R. (1965). A Simplex Method for Function Minimization. The Computer Journal, 7(4), 308-313. doi:10.1093/comjnl/7.4.308Olsson, A., Sandberg, G., & Dahlblom, O. (2003). On Latin hypercube sampling for structural reliability analysis. Structural Safety, 25(1), 47-68. doi:10.1016/s0167-4730(02)00039-5Santonja, F. J., Tarazona, A. C., & Villanueva, R. J. (2008). A mathematical model of the pressure of an extreme ideology on a society. Computers & Mathematics with Applications, 56(3), 836-846. doi:10.1016/j.camwa.2008.01.001Schmitz, J. M., Stotts, A. L., Rhoades, H. M., & Grabowski, J. (2001). Naltrexone and relapse prevention treatment for cocaine-dependent patients. Addictive Behaviors, 26(2), 167-180. doi:10.1016/s0306-4603(00)00098-8Sharomi, O., & Gumel, A. B. (2008). Curtailing smoking dynamics: A mathematical modeling approach. Applied Mathematics and Computation, 195(2), 475-499. doi:10.1016/j.amc.2007.05.012Stotts, A. L., Mooney, M. E., Sayre, S. L., Novy, M., Schmitz, J. M., & Grabowski, J. (2007). Illusory predictors: Generalizability of findings in cocaine treatment retention research. Addictive Behaviors, 32(12), 2819-2836. doi:10.1016/j.addbeh.2007.04.020White, E., & Comiskey, C. (2007). Heroin epidemics, treatment and ODE modelling. Mathematical Biosciences, 208(1), 312-324. doi:10.1016/j.mbs.2006.10.00

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Academic underachievement is a concern of paramount importance in Europe, and particularly in Spain, where around of 30% of the students in the last two courses in high school do not achieve the minimum knowledge academic requirement. In order to analyze this problem, we propose a mathematical model via a system of ordinary differential equations to study the dynamics of the academic performance in Spain. Our approach is based on the idea that both, good and bad study habits, are a mixture of personal decisions and influence of classmates. Moreover, in order to consider the uncertainty in the estimation of model parameters, a bootstrapping approach is employed. This technique permits to forecast model trends in the next few years using confidence intervals. Unfortunately, the obtained results do not suggest improvement in academic performance for the coming years.Cortés López, JC.; Sánchez Sánchez, A.; Santonja, FJ.; Villanueva Micó, RJ. (2013). Non-parametric probabilistic forecasting of academic performance in Spanish high school using an epidemiological modelling approach. Applied Mathematics and Computation. 221(15):648-661. doi:10.1016/j.amc.2013.06.070S6486612211

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