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

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  • 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 $n=2$.
    Mathematics Subject Classification: Primary: 34D23; Secondary: 92B30.


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