Journal Article

A family of models of angiogenesis and anti-angiogenesis anti-cancer therapy

Alberto D'Onofrio and Alberto Gandolfi

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 26, issue 1, pages 63-95
Published in print March 2009 | ISSN: 1477-8599
Published online November 2008 | e-ISSN: 1477-8602 | DOI: http://dx.doi.org/10.1093/imammb/dqn024
A family of models of angiogenesis and anti-angiogenesis anti-cancer therapy

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In this paper we propose a class of models that describe the mutual interaction between tumour growth and the development of tumour vasculature and that generalize existing models. The study is mainly focused on the effect of a therapy that induces tumour vessel loss (anti-angiogenic therapy), with the aim of finding conditions that asymptotically guarantee the eradication of the disease under constant infusion or periodic administration of the drug. Furthermore, if tumour and/or vessel dynamics exhibit time delays, we derive conditions for the existence of Hopf bifurcations. The destabilizing effect of delays on achieving the tumour eradication is also investigated. Finally, global conditions for stability and eradication in the presence of delays are given for some particular cases.

Keywords: angiogenesis; anti-angiogenesis; tumour eradication; stability; delay differential equations

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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