Abstract
In Chap. 12 some mathematical models of social behavior are proposed. To be precise, delayed and stochastic mathematical models are proposed to analyze human behaviors related to some addictions: consumption of alcohol and obesity. An alcohol consumption habit is considered as susceptible to be transmitted by peer pressure or social contact. This fact leads us to propose an epidemiologic-type mathematical model to study this social epidemic. The known nonlinear dynamic model of alcohol consumption is generalized by adding a distributed delay. Sufficient conditions for the existence and stability in probability of the positive equilibrium point of this system by stochastic perturbations are obtained. The research similar to the previous one is applied also to the social obesity epidemic models with distributed delay. The obtained results are illustrated by four figures with numerical simulations of stability regions and trajectories of solutions.
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Shaikhet, L. (2013). Stability of Some Social Mathematical Models with Delay Under Stochastic Perturbations. In: Lyapunov Functionals and Stability of Stochastic Functional Differential Equations. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00101-2_12
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DOI: https://doi.org/10.1007/978-3-319-00101-2_12
Publisher Name: Springer, Heidelberg
Print ISBN: 978-3-319-00100-5
Online ISBN: 978-3-319-00101-2
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