Mulone, Giuseppe; Straughan, Brian A note on heroin epidemics. (English) Zbl 1160.92337 Math. Biosci. 218, No. 2, 138-141 (2009). Summary: We show that the steady states of the E. White and C. Comiskey [Heroin epidemics, treatment and ODE modelling. Math. Biosci. 208, No. 1, 312–324 (2007; Zbl 1116.92062)] model of heroin epidemics are stable. Cited in 46 Documents MSC: 92D30 Epidemiology 34D20 Stability of solutions to ordinary differential equations Keywords:equilibria; stability PDF BibTeX XML Cite \textit{G. Mulone} and \textit{B. Straughan}, Math. Biosci. 218, No. 2, 138--141 (2009; Zbl 1160.92337) Full Text: DOI References: [1] Benedict, B., Modelling alcoholism as a contagious disease: how infected drinking buddies spread problem drinking?, SIAM news, 40, (2007) [2] Deacon, L.; Hughes, S.; Tocque, K.; Bellis, M.A., 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.; Gannon, M., Capture – recapture estimates of the local and national prevalence of problem drug use in Scotland, Int. J. drug policy, 17, 203, (2006) [5] Hethcote, H.W., The mathematics of infectious diseases, SIAM rev., 42, 599, (2000) · Zbl 0993.92033 [6] Legrand, J.; Grais, R.F.; Boelle, P.Y.; Valleron, A.J.; Flahault, A., Understanding the dynamics of ebola epidemics, Epidemiol. infect., 135, 610, (2007) [7] Mulone, G.; Solonnikov, V.A., Linearization principle for a system of equations of mixed type, Nonlinear anal. ser. A, (2009) · Zbl 1178.35061 [8] Nordt, C.; Stohler, R., Estimating heroin epidemics with data of patients in methadone maintenance treatment, collected during a single treatment day, Addiction, 103, 591, (2008) [9] Perko, L., Differential equations and dynamical systems, (2001), Springer New York · Zbl 0973.34001 [10] Sánchez, F.; Wang, X.; Castillo-Cáhvez, C.; Gorman, D.M.; Gruenwald, P.J., Drinking as an epidemic: a simple mathematical model with recovery and relapse, (), 353 [11] Straughan, B., The energy method: stability and nonlinear convection, (2004), Springer New York · Zbl 1032.76001 [12] White, E.; Comiskey, C., Heroin epidemics, treatment and ODE modelling, Math. biosci., 208, 312, (2007) · Zbl 1116.92062 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.