Geodesic
Analysis of a delay differential equations modelling tumor growth with angiogenesis
Mathematica Applicanda, Tome 47 (2019) no. 2, pp. 207-217.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

Angiogenesis is a crucial process for the survival of cancer cells. Due to the rapid growth of the tumor, blood vessels delivering oxygen become insufficient, which leads to hypoxic regions inside the tumor and therefore death of the cells. Cancer cells deal with this problem by stimulating the growth of new vessels, thus providing the necessary amount of oxygen. The understanding of this process allowed to develop antiangiogenic therapy, which attack tumor vasculature instead of cells themselves. It is believed that effective treatment combines antiangiogenic factors with radio- and chemotherapy. Our aim is to construct a mathematical model describing this process, which would further allow to select optimal dosage. In this paper we propose a delay differential model of tumor growth and perform its preliminary analysis. We then introduce a method, which enables further study on this model. The results are illustrated by numerical simulations.
DOI : 10.14708/ma.v47i2.6493
Classification : Primary: 34D20, Secondary: 92C99
Mots-clés : angiogenesis, VEGF, antiangiogenic treatment, delay differential equations, stability analysis 
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Maja Szlenk; Marek Bodnar. Analysis of a delay differential equations modelling tumor growth with angiogenesis. Mathematica Applicanda, Tome 47 (2019) no. 2, pp.  207-217. doi : 10.14708/ma.v47i2.6493. http://geodesic.mathdoc.fr/articles/10.14708/ma.v47i2.6493/

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