A note on heroin epidemics

Mathematical Biosciences

Volumn 218, Issue 2, 2009, Pages 138-141

  Mulone, Giuseppe ^a   Straughan, Brian ^b  

^a UNIVERSITY OF CATANIA   (Italy)

^b DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Equilibria; Heroin epidemics; Stability

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL TECHNIQUES; STATISTICS;

EQUILIBRIA; HEROIN EPIDEMICS; STEADY STATE;

EPIDEMIOLOGY;

DISEASE TREATMENT; DRUG; EPIDEMIC; EQUILIBRIUM;

EID: 62549090964     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2009.01.006     Document Type: Article

References (12)

1. Benedict B. Modelling alcoholism as a contagious disease: how infected drinking buddies spread problem drinking?. SIAM News 40 (2007)
2. In: Deacon L., Hughes S., Tocque K., and Bellis M.A. (Eds). Indications of Public Health in English Regions. 8: Alcohol (2007), Association of Public Health Observatories, New York
3. G. Hay, M. Gannon, J. MacDougall, T. Millar, C. Eastwood, N. McKeganey, Local and national estimates of the prevalence of opiate use and/or crack cocaine use, in: R. Murray, L. Tinsley (Eds.), Measuring Different Aspects of Problem Drug Use: Methodological Developments, N. Singleton, Online Report OLR 16/06. London, Home Office, 2006.
4. Hay G., and Gannon M. Capture-recapture estimates of the local and national prevalence of problem drug use in Scotland. Int. J. Drug Policy 17 (2006) 203
5. Hethcote H.W. The mathematics of infectious diseases. SIAM Rev. 42 (2000) 599
6. Legrand J., Grais R.F., Boelle P.Y., Valleron A.J., and Flahault A. Understanding the dynamics of Ebola epidemics. Epidemiol. Infect. 135 (2007) 610
7. Mulone G., and Solonnikov V.A. Linearization principle for a system of equations of mixed type. Nonlinear Anal. Ser. A (2009) 10.1016/j.na.2008.11.023
8. Nordt C., and Stohler R. Estimating heroin epidemics with data of patients in methadone maintenance treatment, collected during a single treatment day. Addiction 103 (2008) 591
9. Perko L. Differential Equations and Dynamical Systems. third ed. (2001), Springer, New York
10. Sánchez F., Wang X., Castillo-Cáhvez C., Gorman D.M., and Gruenwald P.J. Drinking as an epidemic: a simple mathematical model with recovery and relapse. In: Witkiewitz K., and Alan Marlett G. (Eds). Therapist's Guide to Evidence-Based Relapse Prevention (2007), Academic Press, New York 353
11. Straughan B. The Energy Method: Stability and Nonlinear Convection. second ed. (2004), Springer, New York
12. White E., and Comiskey C. Heroin epidemics, treatment and ODE modelling. Math. Biosci. 208 (2007) 312