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

Abstract

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 ℜ0: if ℜ0 ≤ 1, then the drug-free equilibrium is globally asymptotically stable; if ℜ0 > 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 graphtheoretic 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.