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Dynamics and numerical simulations in a production and development of red blood cells with one delay

Radouane Yafia

Abstract


In this paper we study an unstructured model of a cellular population in the spirit of Grabosh and Heijmans [2] model. The cellular population is described by a system of differential equations with one delay. The basic assumption is that the cell population responsible for the production of blood cells consists of three compartments: the stem cells, the precursor cells, and the blood cells. We prove that the model has two possible steady states and their dynamics (depending on time delay) are studied in term of the local stability. We illustrate our results with numerical simulations for some different values of the time delay.

Keywords


Red blood cells, delayed differential equations, equilibrium point, stability, oscillating solutions.

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