Modelling drug administration regimes for asthma: a Romanian experience

Abstract

In this paper we present a modelling activity, which was a part of the project DQME II 3 and some general observations regarding the maladjustments and rational errors arising in such type of activities.

Classroom Methodologies for Teaching and Learning Ordinary Differential Equations: A Systemic Literature Review and Bibliometric Analysis

“…[21] Others [22] Geometric and qualitative solutions Mathematical modeling Systems: applications for asthma [23] Active learning Scalar: first order [27] Information and communication technology Systems: applications for Chemical reactions [28] Information and communication technology Scalar: first order, second order, graphical solution, Laplace transform [29] Information and communication technology Scalar: first order, freefall problems [30] Project-based learning [31] Projects-based learning Scalar: first order, applications to tumor growth, Gompertz model, graphical solutions, bifurcation [32] Information and communication technology Scalar and systems: several topics [33] Information and communication technology Scalar and systems: first order, Laplace transform, application to chemical reaction and control [34] Information and communication technology Scalar and systems: several topics [39] Traditional methodology, Geometric and qualitative solutions Scalar: first order, applications to exponential decay problems [48] Mathematical modeling Scalar: Newton's law of cooling and laws for velocity, acceleration and volume Table 6. Cont.…”

“…For instance, the order and the non-linearity of the equation which does not permit the universal application of those methods. In our list, 14 articles are focused on exploring the teaching of graphical solution, qualitative behavior and numerical solution of ordinary differential equations [3,4,14,22,39,56,64,[69][70][71][72]84,97,109]. In the articles related to the teaching of qualitative analysis of ordinary differential equations, the focus is mainly in the learning of several concepts like graphical solution, direction fields, stability, and increasing or decreasing behavior of the solution, interpretation of situations based on the behavior of solutions.…”

“…The motivation for innovation in the traditional teaching obey different reasons, at least three of those are given below. First, from the second half of the 20th century until now, the ordinary differential equations have been recognized as useful tools for teaching and learning mathematical models arising in different areas of science like physics, biomathematics, engineering, and chemistry [20][21][22][23][24][25][26]. Second, in our current era, the development of information technologies has strongly influenced and modified the traditional ways of inquiring in science.…”

Mathematics and the Heart: Understanding Cardiac Output

“…Such ideas have been extensively discussed by various authors such as in the special volumes introduced by Ledder [7], and by Kobylski Winkel [6]. Some of the mathematical biology topics for high school and undergraduate curricula that have been addressed in the past include: "Modeling drug administration regimes for asthma by Andras and Szilagyi [1]; "What's my math course got to do with biology?," which discusses an application of Leslie matrices to address age-structured population problems, by Burks et al [2].…”

“…This paper was presented as a module in a one-day workshop for high school teachers. 1 Cardiac output refers to the volume of blood pumped every minute by the heart and is a measure of the effectiveness of to heart as a pump. Since blood carries oxygen (which is needed to produce energy) to all tissues, cardiac output is an important factor in determining the overall physical well-being of a person.…”