J. P. Caulkins, A. Gragnani, G. Feichtinger, G. Tragler:
"High and low frequency oscillations in drug epidemics";
International Journal of Bifurcation and Chaos,
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 shortand
long-run periodicity is reminiscent of the elliptical burstors described by Rubin and Terman
. The existence of such complex behavior including cycles, quasi periodic solutions, and
chaos is proven by means of bifurcation analysis.
Illicit drugs; drug epidemics; dynamical systems; oscillations; bifurcation analysis.
Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.