Threshold dynamics of a delayed multi-group heroin epidemic model in heterogeneous populations

Lili  Liu; Xianning  Liu; Jinliang  Wang

doi:10.3934/dcdsb.2016064

Article Contents

2016, Volume 21, Issue 8: 2615-2630. Doi: 10.3934/dcdsb.2016064

This issue Previous Article Phase transition of oscillators and travelling waves in a class of relaxation systems Next Article Global well-posedness for the two-dimensional equations of nonhomogeneous incompressible liquid crystal flows with nonnegative density

Threshold dynamics of a delayed multi-group heroin epidemic model in heterogeneous populations

1.
Key Laboratory of Eco-environments in Three Gorges Reservoir Region, (Ministry of Education), School of Mathematics and Statistics, Southwest University, Chongqing 400715
2.
School of Mathematical Science, Heilongjiang University, Harbin 150080

Received: March 31, 2015

Revised: May 31, 2016

Published: September 2016

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Abstract

The aim of this paper is to investigate the threshold dynamics of a heroin epidemic in heterogeneous populations. The model is described by a delayed multi-group model, which allows us to model interactions both within-group and inter-group separately. Here we are able to prove the existence of heroin-spread equilibrium and the uniform persistence of the model. The proofs of main results come from suitable applications of graph-theoretic approach to the method of Lyapunov functionals and Krichhoff's matrix tree theorem. Numerical simulations are performed to support the results of the model for the case where $n=2$.

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Mathematics Subject Classification: Primary: 34D23; Secondary: 92B30.

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