Steady-State Analysis of a Two Dimensional Model for Tumor Angiogenesis in the Absence of Endothelial Cell Proliferation

Serdal Pamuk and Bushra Bajjah
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Serdal Pamuk: Department of Mathematics, University of Kocaeli, Umuttepe Campus, 41800, Kocaeli – Turkey
Bushra Bajjah: Department of Mathematics, University of Kocaeli, Umuttepe Campus, 41800, Kocaeli – Turkey

Academic Journal of Applied Mathematical Sciences, 2016, vol. 2, issue 9, 102-108

Abstract: This paper is an extension of the work done in [S. Pamuk, Qualitative Analysis of a Mathematical Model for Capillary Formation in Tumor Angiogenesis, Math. Models Methods Appl. Sci. 13 (1) (2003) 19-33] to a further 2D-mathematical analysis of a model for tumor angiogenesis in the absence of endothelial cell proliferation term. We actually obtain the long time dynamics of endothelial cells in the extra cellular matrix under some assumptions and using the results of a 1D-mathematical analysis. Also, the stability of the steady-state solution is studied. Some figures obtained from the numerical results are presented.

Keywords: Angiogenesis; Long-time dynamics; Steady-state solution; Mathematical analysis. (search for similar items in EconPapers)
Date: 2016
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