 Global asymptotic properties of a heroin epidemic model with treat-ageBin Fang, Xue-Zhi Li, Maia Martcheva and Li-Ming Cai Applied Mathematics and Computation, 2015, vol. 263, issue C, 315-331 Abstract: In this paper, a model for the use of heroin with treat-age is formulated based on the principles of mathematical epidemiology. The model accounts for relapse rate that depends on how long the host has been in treatment for heroin addiction. An explicit formula for the reproductive number of the heroin spread is obtained. By using the method of Lyapunov functional, we established the dynamical properties of the heroin epidemic model, and the results show that the global dynamics of the model is completely determined by the basic reproduction number. It is shown that the drug-free equilibrium is locally and globally asymptotically stable if the basic reproduction number is less than one. In addition, the heroin spread system is uniform persistence and the unique drug spread equilibrium is locally and globally asymptotically stable if the basic reproduction number is greater than one. Keywords: Heroin epidemic model; Treat-age; Drug-free equilibrium; Drug spread equilibrium; Basic reproduction number; Lyapunov functional (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:263:y:2015:i:c:p:315-331 DOI: 10.1016/j.amc.2015.04.055 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.