ANALYSIS OF THE BINGE DRINKING MODELS WITH DEMOGRAPHICS AND NONLINEAR INFECTIVITY ON NETWORKS

Hong Xiang; Yanyan Wang; Haifeng Huo

doi:10.11948/2018.1535

2018 Volume 8 Issue 5

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Hong Xiang, Yanyan Wang, Haifeng Huo. ANALYSIS OF THE BINGE DRINKING MODELS WITH DEMOGRAPHICS AND NONLINEAR INFECTIVITY ON NETWORKS[J]. Journal of Applied Analysis & Computation, 2018, 8(5): 1535-1554. doi: 10.11948/2018.1535

Citation:

Hong Xiang, Yanyan Wang, Haifeng Huo. ANALYSIS OF THE BINGE DRINKING MODELS WITH DEMOGRAPHICS AND NONLINEAR INFECTIVITY ON NETWORKS[J]. Journal of Applied Analysis & Computation, 2018, 8(5): 1535-1554. doi: 10.11948/2018.1535

ANALYSIS OF THE BINGE DRINKING MODELS WITH DEMOGRAPHICS AND NONLINEAR INFECTIVITY ON NETWORKS

Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, China

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Abstract

Abstract

Two new binge drinking models incorporating demographics on different weighted networks are investigated. First, the dynamics of the drinking model with the linear infectivity φ(k)=k on the unweighted network is investigated. The basic reproduction number R₀ and the uniqueness and stability of all the equilibria are derived. Second, the model with the nonlinear infectivity φ(k)=k^a(0 < a < 1) and two kinds of weights is introduced, and stability of all the equilibria is studied. At last, some simulations are presented to illustrate our analytic results. Our results show that the spread of drinking behaviors on the fixed weighted network is the most easily to break out, and the infectivity exponent also has a greater effect on the spread of drinking behaviors than that of the weight exponent.
- Binge drinking /
- demographics /
- stability /
- nonlinear infectivity /
- weight networks
MSC: 92D25

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References

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