Communications in Nonlinear Science and Numerical Simulation
Letter to the EditorPopulation dynamics in educational institutions considering the student satisfaction
Introduction
Forecasting the number of enrolled students in the coming years is a major concern of any educational establishment, because such a number affects its resources and expenses (e.g. [7]). In this context, it is relevant, for instance, to estimate the probability of a student dropping out of a course before obtaining the diploma (e.g. [18]) and to examine the influence of good and bad study habits on the academic performance (e.g. [5]) and, consequently, on the dropout rate.
Here, I propose and analyze a second-order system of difference equations that represent the population dynamics in educational institutions, by taking into account the institutional quality perceived by the students. In this model, at every time instant, every student is in one of two states: satisfied or dissatisfied. Satisfaction and dissatisfaction can be propagated through personal contacts as contagious diseases or social behaviors (e.g. [5], [8], [16], [17]). Students are also able of autonomously shifting from satisfied to dissatisfied, or vice versa. Satisfied students drop out only due to financial or health problems; dissatisfied students can abandon the educational institution due to financial or health problems, deficient academic achievement, or negative perception of the learning environment (e.g. [4], [6]). In addition, both groups of students can complete their degrees. The aim of this study based on the above assumptions is to evaluate how academic and administrative measures for quality enhancement can affect the composition of the student population. I did not find in the literature any study with this approach. Obviously, student satisfaction in the real world can be determined from interviews, questionnaires, surveys.
This paper is organized as follows. In Section 2, the discrete-time system is described, and the steady-state solutions and the corresponding stabilities are analytically derived for two particular choices of student influx. In Section 3, results of numerical simulations are presented to further explore the model dynamics. In Section 4, the possible relevance of this work is stressed and discussed from an institutional management point of view.
Section snippets
Model and analytical results
Consider an educational establishment, like a school, a college, a university, or even a fitness center (which receives and loses students/users on a daily basis). Let Φ(t) be the amount of students admitted at the time step t (which can be conveniently measured in days, weeks, months, semesters, or years). The numbers of satisfied and dissatisfied students at t are denoted by S(t) and D(t), respectively. Assume that both groups of students are homogeneously distributed over the space; that is,
Numerical results
In order to illustrate the model dynamics, numerical simulations were performed. In all figures, thin line represents S(t); thick line, D(t).
Figs. 1(a)–(i) exhibit the dynamic behaviors obtained from Eqs. (1) and (2) for and . For instance, means that 15% of the S-students earn their diplomas at each time step. The values of a, c, r1, and r2 are varied in these figures to investigate the dissatisfaction spread. In Fig. 1(a),
Discussion
Several managerial and governmental issues have been theoretically investigated and some of these works have been based on discrete-time approaches. For instance, the effects of positive and negative behavior features of employees on the workplace dynamics were examined with a cellular automaton model [13]; the impact of cash transfer programs implemented in several countries to improve the education and health of children was studied with multi-agent systems [15].
Here, an analytical model
Acknowledgments
The author is partially supported by CNPq. The author would like to thank Renê de Ávila Mendes for the inspiring conversations.
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