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Abstract
In this paper, an alcoholism model of SEAR type with different susceptibilities due to public health education is investigated, with the form of continuous differential equations as well as discrete differential equations by applying the Mickens nonstandard finite difference (NSFD) scheme to the continuous equations. Threshold dynamics of the continuous model are performed by constructing Lyapunov functions. The analysis of a discrete model indicates that the alcohol-free equilibrium is globally asymptotically stable if the basic reproductive number R0<1, and conversely, the alcohol-present equilibrium is globally asymptotically stable if R0>1, revealing the consistency and efficiency of the discrete model to preserve the dynamical properties of the corresponding continuous model. In addition, stability preserving and the impact of the parameters related with public health education are conducted by numerical simulations.
Highlights
Alcohol abuse is a major public health concern due to its potential negative health and social effect, especially among college students. ere was evidence showing that more than 40% of college students have experienced alcoholism [1, 2], and it has been observed that binge drinking and drinking behaviors have caused negative effects in different levels on students’ academic study, social relations, risk-taking, and health [3, 4]
We investigated the threshold dynamics of an SEAR alcoholism model with the form of continuous equations and discrete equations, noting that the discrete model is formulated by applying the Michens nonstandard finite difference scheme to the corresponding continuous model
With this method of discretization, as demonstrated by the theoretical and numerical results obtained in this paper, the dynamical properties of the continuous system can be preserved with much high efficiency when compared with the traditional schemes such as forward Euler and Runge–Kutta, which sometimes fail generating oscillations, bifurcations, and chaos, and even result in false steady states [35, 36]
Summary
Alcohol abuse is a major public health concern due to its potential negative health and social effect, especially among college students. ere was evidence showing that more than 40% of college students have experienced alcoholism [1, 2], and it has been observed that binge drinking and drinking behaviors have caused negative effects in different levels on students’ academic study, social relations, risk-taking, and health [3, 4]. Ere was evidence showing that more than 40% of college students have experienced alcoholism [1, 2], and it has been observed that binge drinking and drinking behaviors have caused negative effects in different levels on students’ academic study, social relations, risk-taking, and health [3, 4]. In view of alcohol abuse among students on and around college campuses, there have been compartmental models established to study the role of environmental factors on the dynamics of this specific drinking group [13, 15]. To account for the influence of public health education on the transmission of alcohol consumption, a general nonlinear incidence is utilized in our models, which is different from that in [20].
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