Epidemic dynamics on a delayed multi-group heroin epidemic model with nonlinear incidence rate

For a multi`-group Heroin epidemic model with nonlinear incidence rate and distributed delays, we study some aspects of its global dynamics. By a rigorous analysis of the model, we establish that the model demonstrates a sharp threshold property, completely determined by the values of R-0: if R-0 < 1, then the drug-free equilibrium is globally asymptotically stable; if R-0 > 1, then there exists a unique endemic equilibrium and it is globally asymptotically stable. A matrix-theoretic method based on the Perron eigenvector is used to prove the global asymptotic stability of the drug-free equilibrium and a graph theoretic method based on Kirchhoff's matrix tree theorem was used to guide the construction of Lyapunov functionals for the global asymptotic stability of the endemic equilibrium. (C) 2016 All rights reserved.