| Volume 6, Number 2, 2016, Pages 429-442 DOI：10.11948/2016032 |
| Global dynamical analysis of a heroin epidemic model on complex networks |
| Junyuan Yang,Lianhua Wang,Xiaoxia Li,Fengqin Zhang |
| Keywords:Heroin model, complex networks, global stability |
| Abstract: |
| In this paper, a heroin epidemic model on complex networks is proposed.
By the next generation matrix, the basic reproduction number $R_0$ is obtained. If $R_0<1$, then the drug-free equilibrium is globally asymptotically stable. If $R_0>1$, there is an unique endemic equilibrium and it is also globally asymptotically stable. Our results show that if the degree of the network is large enough, the drug transmission always spreads. Sensitivity analysis of the basic reproduction number with the various parameters in the model are carried out to verify the important effects for control the drug transmission. Some simulations illustrate our theoretical results |
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