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

Hong Xiang | Zendy; Yanyan Wang | Zendy; HaiFeng Huo | Zendy

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

Author(s) -

Hong Xiang,

Yanyan Wang,

HaiFeng Huo

Publication year - 2018

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2018.1535

Subject(s) - infectivity , uniqueness , demographics , nonlinear system , exponent , stability (learning theory) , mathematics , statistics , demography , computer science , physics , mathematical analysis , biology , virology , virus , quantum mechanics , sociology , linguistics , philosophy , machine learning

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(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.

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