?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4134%2F&rft.title=Dynamics+of+Drug+Consumption%3A+a+Theoretical+Model&rft.creator=Gragnani%2C+A.&rft.creator=Feichtinger%2C+G.&rft.creator=Rinaldi%2C+S.&rft.description=A+continuous+time+model+is+proposed+to+describe+the+dynamics+of+drug+consumption+in+a+given+country.+The+model+has+two+state+variables%2C+addicts+and+dealers%2C+and+eleven+parameters%2C+including+the+total+effort+exerted+by+the+State%2C+which+is+considered+as+control+parameter.+The+model+is+highly+nonlinear+and+the+analysis+shows+that+it+is+characterized+by+a+transcritical+and+a+fold+bifurcation.+This+implies+that+for+intermediate+values+of+the+State's+effort+the+model+has+two+stable+equilibria%2C+one+trivial%2C+corresponding+to+the+absence+of+drugs%2C+and+one+positive%2C+corresponding+to+drug+consumption.+On+the+contrary%2C+for+low+and+high+values+of+the+effort+only+one+of+the+two+equilibria+is+stable.+This+suggests+a+two-step+control+policy.+First%2C+exert+a+very+high+effort+for+a+few+years%2C+so+that+the+system+has+the+time+to+approach+the+trivial+equilibrium%2C+and+then+reduce+the+effort+but+maintain+it+sufficiently+high+so+that+drug+consumption+cannot+rise+anymore.+Interesting+results+on+the+role+played+by+the+price+of+the+drug+and+the+severity+of+the+punishment+inflicted+to+dealers%2C+as+well+as+on+the+allocation+of+the+effort+between+therapy+and+police%2C+have+also+been+obtained.&rft.publisher=WP-94-077&rft.date=1994-08&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4134%2F1%2FWP-94-077.pdf&rft.identifier=++Gragnani%2C+A.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F1294.html%3E%2C+Feichtinger%2C+G.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F2589.html%3E%2C+%26+Rinaldi%2C+S.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F253.html%3E++(1994).++Dynamics+of+Drug+Consumption%3A+a+Theoretical+Model.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-94-077+++++