{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,11]],"date-time":"2024-02-11T08:40:22Z","timestamp":1707640822082},"reference-count":36,"publisher":"World Scientific Pub Co Pte Ltd","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2006,11]]},"abstract":"<jats:p>We extend the two-dimensional model of drug use introduced in [Behrens et al., 1999, 2000, 2002] by considering two additional states that represent in more detail newly initiated (\"light\") users' response to the drug experience. Those who dislike the drug quickly \"quit\" and briefly suppress initiation by others. Those who like the drug progress to ongoing (\"moderate\") use, from which they may or may not escalate to \"heavy\" or dependent use. Initiation is spread contagiously by light and moderate users, but is moderated by the drug's reputation, which is a function of the number of unhappy users (recent quitters + heavy users). The model reproduces recent prevalence data reasonably well from the U.S. cocaine epidemic, with one pronounced peak followed by decay toward a steady state. However, minor variation in parameter values yields both long-run periodicity with a period akin to the gap between the first U.S. cocaine epidemic (peak ~1910) and the current one (peak ~1980), as well as short-run periodicity akin to that observed in data on youthful use for a variety of substances. The combination of short- and long-run periodicity is reminiscent of the elliptical burstors described by Rubin and Terman [2002]. The existence of such complex behavior including cycles, quasi periodic solutions, and chaos is proven by means of bifurcation analysis.<\/jats:p>","DOI":"10.1142\/s0218127406016781","type":"journal-article","created":{"date-parts":[[2007,2,28]],"date-time":"2007-02-28T08:27:39Z","timestamp":1172651259000},"page":"3275-3289","source":"Crossref","is-referenced-by-count":4,"title":["HIGH AND LOW FREQUENCY OSCILLATIONS IN DRUG EPIDEMICS"],"prefix":"10.1142","volume":"16","author":[{"given":"JONATHAN P.","family":"CAULKINS","sequence":"first","affiliation":[{"name":"H. John Heinz III School of Public Policy Management, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ALESSANDRA","family":"GRAGNANI","sequence":"additional","affiliation":[{"name":"Department of Electronics and Information, Politecnico of Milan, Via Ponzio 34\/5, 20133 Milan, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"GUSTAV","family":"FEICHTINGER","sequence":"additional","affiliation":[{"name":"Institute for Mathematical Methods in Economics, Vienna University of Technology, Argentinierstrasse 8\/105-4, A\u20131040 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"GERNOT","family":"TRAGLER","sequence":"additional","affiliation":[{"name":"Institute for Mathematical Methods in Economics, Vienna University of Technology, Argentinierstrasse 8\/105-4, A\u20131040 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5564(99)00016-4"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.46.3.333.12068"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-1889(01)00003-3"},{"key":"rf5","first-page":"179","volume":"1","author":"Brill H.","journal-title":"Seminars in Psychiatry"},{"key":"rf6","doi-asserted-by":"crossref","DOI":"10.7249\/MR923","volume-title":"An Ounce of Prevention, a Pound of Uncertainty: The Cost-Effectiveness of School-Based Drug Prevention Program","author":"Caulkins J. P.","year":"1999"},{"key":"rf7","volume-title":"School-Based Drug Prevention: What Kind of Drug Use Does it Prevent?","author":"Caulkins J. P.","year":"2002"},{"key":"rf8","doi-asserted-by":"crossref","DOI":"10.7249\/IP246","volume-title":"Drug Use and Drug Policy Futures: Insights from a Colloquium","author":"Caulkins J. P.","year":"2003"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/s10729-004-7540-4"},{"key":"rf10","unstructured":"J. P.\u00a0Caulkins, Substance Use: Individual Behavior, Social Interactions, Markets, and Politics, Advances in Health Economics and Health Services\u00a016, eds. B.\u00a0Lindgren and M.\u00a0Grossman (Elsevier, 2005)\u00a0pp. 407\u2013439."},{"key":"rf11","doi-asserted-by":"crossref","DOI":"10.4159\/9780674029903","volume-title":"Forces of Habit: Drugs and the Making of the Modern World","author":"Courtwright D.","year":"2001"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1111\/j.1360-0443.2005.01094.x"},{"key":"rf13","volume-title":"Modeling the Demand for Cocaine","author":"Everingham S. S.","year":"1994"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/0038-0121(95)00018-6"},{"key":"rf17","volume-title":"The Hardest Drug: Heroin and Public Policy","author":"Kaplan J."},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1080\/09595230410001645600"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-0659-4_19"},{"key":"rf20","unstructured":"A. I.\u00a0Khibnik, Mathematics and Modelling, eds. Yu. G.\u00a0Zarhin and A. D.\u00a0Bazykin (Pushchino: Center of Biological Research of the U.S.S.R. Academy of Sciences, 1990)\u00a0pp. 162\u2013197."},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(93)90294-B"},{"key":"rf22","volume-title":"Against Excess: Drug Policy for Results","author":"Kleiman M. A. R.","year":"1992"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2421-9"},{"key":"rf24","volume-title":"The Theory of Matrices","author":"Lancaster P.","year":"1985"},{"key":"rf25","first-page":"15","volume":"1","author":"Marotta M.","journal-title":"Bull. Narcotics"},{"key":"rf26","volume-title":"The American Disease","author":"Musto D. F.","year":"1987"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1016\/S0376-8716(01)00207-1"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(99)00234-1"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.2105\/AJPH.85.8_Pt_1.1059"},{"key":"rf30","volume-title":"The Alcoholic Republic: An American Tradition","author":"Rorabaugh W. J.","year":"1979"},{"key":"rf31","volume-title":"Handbook of Dynamical Systems, Vol. 2: Toward Applications","author":"Rubin J. E.","year":"2002"},{"key":"rf32","doi-asserted-by":"crossref","DOI":"10.7249\/MR331","volume-title":"Controlling Cocaine. Supply versus Demand Programs","author":"Rydell C. P.","year":"1994"},{"key":"rf33","doi-asserted-by":"publisher","DOI":"10.1287\/opre.44.5.687"},{"key":"rf34","doi-asserted-by":"crossref","DOI":"10.56021\/9780801862304","volume-title":"Cocaine: From Medical Marvel to Modern Menace in the United States, 1884\u20131920","author":"Spillane J.","year":"2000"},{"key":"rf35","volume-title":"Nonlinear Dynamics and Chaos","author":"Strogatz S. H.","year":"1994"},{"key":"rf37","doi-asserted-by":"publisher","DOI":"10.1287\/opre.49.3.352.11215"},{"key":"rf38","volume-title":"Cocaine Changes: The Experience of Using and Quitting","author":"Waldorf D.","year":"1991"},{"key":"rf39","doi-asserted-by":"publisher","DOI":"10.1046\/j.1360-0443.2003.00248.x"},{"key":"rf40","doi-asserted-by":"publisher","DOI":"10.1016\/S0038-0121(03)00027-2"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127406016781","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,11]],"date-time":"2024-02-11T08:07:15Z","timestamp":1707638835000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127406016781"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,11]]},"references-count":36,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,11]]}},"alternative-id":["10.1142\/S0218127406016781"],"URL":"https:\/\/doi.org\/10.1142\/s0218127406016781","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,11]]}}}