 Analysis of an age-structured multi-group heroin epidemic modelJinliang Wang, Jing Wang and Toshikazu Kuniya Applied Mathematics and Computation, 2019, vol. 347, issue C, 78-100 Abstract: This paper is concerned with the mathematical analysis of an age-structured multi-group heroin epidemic model, which can be used to describe the spread of heroin habituation and addiction in heterogeneous environment. Under general assumptions on the different level of susceptibility and the relapse to frequent heroin use, we establish sharp criteria for heroin spreading and vanishing. We rigorously investigate the well-posedness of the model, the existence of equilibria, the asymptotic smoothness of solution orbits, and the global stability of equilibria. Specifically, we rigorously show that the drug-free equilibrium is globally asymptotically stable if a threshold value ℜ0 is less than one, and the unique drug-endemic equilibrium is globally attractive if ℜ0 is greater than one. In the proofs of global stability of equilibria, we construct suitable Lyapunov functions by using a graph-theoretic method. Keywords: Heroin epidemic; Multi-group model; Age-structured model; Global stability; Lyapunov functions (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:347:y:2019:i:c:p:78-100 DOI: 10.1016/j.amc.2018.11.012 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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