GLOBAL DYNAMICAL ANALYSIS OF A HEROIN EPIDEMIC MODEL ON COMPLEX NETWORKS

Junyuan Yang; Lianhua Wang; Xiaoxia Li; Fengqin Zhang

doi:10.11948/2016032

2016 Volume 6 Issue 2

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Junyuan Yang, Lianhua Wang, Xiaoxia Li, Fengqin Zhang. GLOBAL DYNAMICAL ANALYSIS OF A HEROIN EPIDEMIC MODEL ON COMPLEX NETWORKS[J]. Journal of Applied Analysis & Computation, 2016, 6(2): 429-442. doi: 10.11948/2016032

Citation:

Junyuan Yang, Lianhua Wang, Xiaoxia Li, Fengqin Zhang. GLOBAL DYNAMICAL ANALYSIS OF A HEROIN EPIDEMIC MODEL ON COMPLEX NETWORKS[J]. Journal of Applied Analysis & Computation, 2016, 6(2): 429-442. doi: 10.11948/2016032

GLOBAL DYNAMICAL ANALYSIS OF A HEROIN EPIDEMIC MODEL ON COMPLEX NETWORKS

1 Department of Applied Mathematics, Yuncheng University, Fudan West Street, 044000 Yuncheng, P. R China;
2 Complex Sciences Research Center, Shanxi University, Wucheng Road, 030051, Taiyuan, P. R. China

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Abstract

Abstract

In this paper, a heroin epidemic model on complex networks is proposed. By the next generation matrix, the basic reproduction number R₀ is obtained. If R₀<1, then the drug-free equilibrium is globally asymptotically stable. If R₀>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.
- Heroin model /
- complex networks /
- global stability
MSC: 92D25;92D30

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References

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