American Institute of Mathematical Sciences

Advanced
2006, 3(1): 249-266. doi: 10.3934/mbe.2006.3.249

Raves, clubs and ecstasy: the impact of peer pressure

Baojun Song 1, , Melissa Castillo-Garsow 2, , Karen R. Ríos-Soto 3, , Marcin Mejran 4, , Leilani Henso 5, and  Carlos Castillo-Chavez 6,

1. 

Department of Mathematical Sciences, Montclair State University, Upper Montclair, NJ 07043
2. 

American Studies & African American Studies, Graduate Affiliate, Ethnicity, Race & Migration Program, Yale University, New Haven, CT 06520, United States
3. 

Department of Biological Statistics and Computational Biology, Cornell University, Ithaca, NY 14850, United States
4. 

Department of Mathematics and Computer Science, Stanford University, Stanford, CA 94309, United States
5. 

Department of Mathematics, Howard University, Washignton DC, 20059, United States
6. 

Mathematics, Computational and Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287

Received  February 2005 Revised  May 2005 Published  November 2005

Ecstasy has gained popularity among young adults who frequent raves and nightclubs. The Drug Enforcement Administration reported a 500 percent increase in the use of ecstasy between 1993 and 1998. The number of ecstasy users kept growing until 2002, years after a national public education initiative against ecstasy use was launched. In this study, a system of differential equations is used to model the peer-driven dynamics of ecstasy use. It is found that backward bifurcations describe situations when sufficient peer pressure can cause an epidemic of ecstasy use. Furthermore, factors that have the greatest influence on ecstasy use as predicted by the model are highlighted. The effect of education is also explored, and the results of simulations are shown to illustrate some possible outcomes.
Keywords: drug abuse, dynamical models, global dynamics, peer pressure, bifurcation..
Mathematics Subject Classification: 37N25, 91C20, 37G1.
Citation: Baojun Song, Melissa Castillo-Garsow, Karen R. Ríos-Soto, Marcin Mejran, Leilani Henso, Carlos Castillo-Chavez. Raves, clubs and ecstasy: the impact of peer pressure. Mathematical Biosciences & Engineering, 2006, 3 (1) : 249-266. doi: 10.3934/mbe.2006.3.249
[1]

Lambertus A. Peletier. Modeling drug-protein dynamics. Discrete & Continuous Dynamical Systems - S, 2012, 5 (1) : 191-207. doi: 10.3934/dcdss.2012.5.191
[2]

Ting-Hui Yang, Weinian Zhang, Kaijen Cheng. Global dynamics of three species omnivory models with Lotka-Volterra interaction. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2867-2881. doi: 10.3934/dcdsb.2016077
[3]

Yilei Tang. Global dynamics and bifurcation of planar piecewise smooth quadratic quasi-homogeneous differential systems. Discrete & Continuous Dynamical Systems, 2018, 38 (4) : 2029-2046. doi: 10.3934/dcds.2018082
[4]

Marzia Bisi, Tommaso Ruggeri, Giampiero Spiga. Dynamical pressure in a polyatomic gas: Interplay between kinetic theory and extended thermodynamics. Kinetic & Related Models, 2018, 11 (1) : 71-95. doi: 10.3934/krm.2018004
[5]

Carlos Castillo-Chavez, Baojun Song. Dynamical Models of Tuberculosis and Their Applications. Mathematical Biosciences & Engineering, 2004, 1 (2) : 361-404. doi: 10.3934/mbe.2004.1.361
[6]

Linda J. S. Allen, P. van den Driessche. Stochastic epidemic models with a backward bifurcation. Mathematical Biosciences & Engineering, 2006, 3 (3) : 445-458. doi: 10.3934/mbe.2006.3.445
[7]

Mette S. Olufsen, Ali Nadim. On deriving lumped models for blood flow and pressure in the systemic arteries. Mathematical Biosciences & Engineering, 2004, 1 (1) : 61-80. doi: 10.3934/mbe.2004.1.61
[8]

Jian-Jhong Lin, Weiming Wang, Caidi Zhao, Ting-Hui Yang. Global dynamics and traveling wave solutions of two predators-one prey models. Discrete & Continuous Dynamical Systems - B, 2015, 20 (4) : 1135-1154. doi: 10.3934/dcdsb.2015.20.1135
[9]

Xueli Bai, Fang Li. Global dynamics of competition models with nonsymmetric nonlocal dispersals when one diffusion rate is small. Discrete & Continuous Dynamical Systems, 2020, 40 (6) : 3075-3092. doi: 10.3934/dcds.2020035
[10]

Xiaomei Feng, Zhidong Teng, Fengqin Zhang. Global dynamics of a general class of multi-group epidemic models with latency and relapse. Mathematical Biosciences & Engineering, 2015, 12 (1) : 99-115. doi: 10.3934/mbe.2015.12.99
[11]

Gui-Qiang G. Chen, Qin Wang, Shengguo Zhu. Global solutions of a two-dimensional Riemann problem for the pressure gradient system. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021014
[12]

Hanchun Yang, Meimei Zhang, Qin Wang. Global solutions of shock reflection problem for the pressure gradient system. Communications on Pure & Applied Analysis, 2020, 19 (6) : 3387-3428. doi: 10.3934/cpaa.2020150
[13]

Anna Lisa Amadori. Global bifurcation for the Hénon problem. Communications on Pure & Applied Analysis, 2020, 19 (10) : 4797-4816. doi: 10.3934/cpaa.2020212
[14]

Robert Skiba, Nils Waterstraat. The index bundle and multiparameter bifurcation for discrete dynamical systems. Discrete & Continuous Dynamical Systems, 2017, 37 (11) : 5603-5629. doi: 10.3934/dcds.2017243
[15]

Dan Liu, Shigui Ruan, Deming Zhu. Bifurcation analysis in models of tumor and immune system interactions. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 151-168. doi: 10.3934/dcdsb.2009.12.151
[16]

Qi Deng, Zhipeng Qiu, Ting Guo, Libin Rong. Modeling within-host viral dynamics: The role of CTL immune responses in the evolution of drug resistance. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3543-3562. doi: 10.3934/dcdsb.2020245
[17]

Xinsheng Wang, Weisheng Wu, Yujun Zhu. Local unstable entropy and local unstable pressure for random partially hyperbolic dynamical systems. Discrete & Continuous Dynamical Systems, 2020, 40 (1) : 81-105. doi: 10.3934/dcds.2020004
[18]

Lora Billings, Erik M. Bollt, David Morgan, Ira B. Schwartz. Stochastic global bifurcation in perturbed Hamiltonian systems. Conference Publications, 2003, 2003 (Special) : 123-132. doi: 10.3934/proc.2003.2003.123
[19]

Bernold Fiedler. Global Hopf bifurcation in networks with fast feedback cycles. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 177-203. doi: 10.3934/dcdss.2020344
[20]

Todd Young. A result in global bifurcation theory using the Conley index. Discrete & Continuous Dynamical Systems, 1996, 2 (3) : 387-396. doi: 10.3934/dcds.1996.2.387

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (190)
  • HTML views (0)
  • Cited by (26)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences