Analysis of the binge drinking models with demographics and nonlinear infectivity on networks. (English) Zbl 1457.92183
Summary: Two new binge drinking models incorporating demographics on different weighted networks are investigated. First, the dynamics of the drinking model with the linear infectivity \(\varphi(k)=k\) on the unweighted network is investigated. The basic reproduction number \(R_0\) and the uniqueness and stability of all the equilibria are derived. Second, the model with the nonlinear infectivity \(\varphi(k)=k^a\) (\(0<a<1\)) 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.
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