# American Institute of Mathematical Sciences

May  2014, 19(3): 715-733. doi: 10.3934/dcdsb.2014.19.715

## Global stability for a heroin model with two distributed delays

 1 Beijing Institute of Information and Control, Beijing 100037, China 2 Department of Mathematics, Xinyang Normal University, Xinyang 464000, China 3 Department of Mathematics, University of Florida, 358 Little Hall, PO Box 118105, Gainesville

Received  July 2013 Revised  October 2013 Published  February 2014

In this paper, we consider global stability for a heroin model with two distributed delays. The basic reproduction number of the heroin spread is obtained, which completely determines the stability of the equilibria. Using the direct Lyapunov method with Volterra type Lyapunov function, we show that the drug use-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.
Citation: Bin Fang, Xue-Zhi Li, Maia Martcheva, Li-Ming Cai. Global stability for a heroin model with two distributed delays. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 715-733. doi: 10.3934/dcdsb.2014.19.715
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