The term mathematical modelling covers a wide range of activities. These are not only purely mathematical skills but also skills referring toa framework of modelled situation. For this reason, acquiring the skills of mathematical modelling brings a number of teaching benefits. This ability is connected with necessary competencies related to mathematical modelling. Mathematics students – prospect teachers of mathematics, should acquire these skills before they start teaching mathematical modelling. Is it really so? The paper presents the results of the research on competencies in students’mathematical modelling abilities. We show in what way prospect teachers are able to learn the elements of mathematical modelling on their own. Ther esearch proves the need to review the issue of mathematical modelling in the training of mathematics teachers.
We investigate a mathematical model of population dynamics for a population of two sexes (male and female) in which new individuals are conceived in a process of mating between individuals of opposed sexes and their appearance is postponed by a period of gestation. The model is a system of two partial differential equations with delay which are additionally coupled by mathematically complicated boundary conditions. We show that this model has a global solution. We also analyze stationary ('permanent') solutions and show that such solutions exist if the model parameters satisfy two nonlinear relations.
W artykule analizujemy nową wersję modelu opisującego efekt nabytej lekooporności, który zaproponowaliśmy w pracy Bodnar & Foryś (2017). Oryginalny model powstał w oparciu o idee przedstawione w artykule Pérez-García i in. (2015). W bieżącej pracy włączamy do modelu dodatkowy składnik opisujący bezpośrednią śmiertelność komórek uszkodzonych. Okazuje się, że dynamika tak zmienionego modelu jest analogiczna, jak w przypadku drugiego modelu rozważanego przez nas, który z kolei powstał w oparciu o idee Olliera i in. (2017). Dynamika modelu została przeanalizowana dla parametrów odzwierciedlających wzrost glejaka niskiego stopnia, przy czym analizowaliśmy wpływ zmian poszczególnych parametrów na tę dynamikę.
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In this paper we present a version of a simple mathematical model of acquiring drug resistance which was proposed in Bodnar and Foryś (2017). We based the original model on the idea coming from Pérez-García et al. (2015). Now, we include the explicit death term into the system and show that the dynamics of the new version of the model is the same as the dynamics of the second model considered by us and based on the idea of Ollier et al. (2017). We discuss the model dynamics and its dependence on the model parameters on the example of gliomas.
In this paper we present several examples of simple dynamical systemsdescribing various real processes. We start from well know Fibonaccisequence, through Lotka-Volterra model of prey-predator system, love affairdynamics, ending with modelling of tumour growth.
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