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Global stability for a heroin model with age-dependent susceptibility

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Abstract

This paper considers global asymptotic properties for an age-structured model of heroin use based on the principles of mathematical epidemiology where the incidence rate depends on the age of susceptible individuals. The basic reproduction number of the heroin spread is obtained. It completely determines the stability of equilibria. By using the direct Lyapunov method with Volterra type Lyapunov function, the authors show that the drug-free equilibrium is globally asymptotically stable if the basic reproduction number is less than one, and the unique drug spread equilibrium is globally asymptotically stable if the basic reproduction number is greater than one.

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Authors and Affiliations

  1. Department of Mathematics, Xinyang Normal University, Xinyang, 464000, China

    Bin Fang, Xuezhi Li & Liming Cai

  2. Beijing Institute of Information and Control, Beijing, 100037, China

    Bin Fang

  3. Department of Mathematics, University of Florida, 358 Little Hall, PO Box 118105, Gainesville, FL, 32611–8105, USA

    Maia Martcheva

Authors
  1. Bin Fang
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  2. Xuezhi Li
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  3. Maia Martcheva
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  4. Liming Cai
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Corresponding author

Correspondence to Bin Fang.

Additional information

This research was supported partially by the National Natural Science Foundation of China under Grant Nos. 11271314, 11371305.

This paper was recommended for publication by Editor FENG Dexing.

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Fang, B., Li, X., Martcheva, M. et al. Global stability for a heroin model with age-dependent susceptibility. J Syst Sci Complex 28, 1243–1257 (2015). https://doi.org/10.1007/s11424-015-3243-9

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  • DOI: https://doi.org/10.1007/s11424-015-3243-9

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