Author:
Díaz-Marín Homero,Osuna Osvaldo
Abstract
In this work, we consider the dynamics of a model for tumor volume growth under a drug periodic treatment targeting the process of angiogenesis within the vascularized cancer tissue. We give sufficient conditions for the existence and uniqueness of a global attractor consisting of a periodic solution. This conditions happen to be satisfied by values of the parameters tested for realistic experimental data. Numerical simulations are provided illustrating our findings.
Publisher
Universidad Nacional de Colombia
Reference9 articles.
1. K. D. Argyri and et. al., Numerical simulation of vascular tumour growth under antiangiogenic treatment: addressing the paradigm of single-agent bevacizumab therapy with the use of experimental data, Biology direct 11 (2016), no. 1, 31.
2. A. D'Onofrio and A. Gandolfi, Tumor eradication by antiangiogenic therapy: analysis and extensions of the model by hahnfeldt et at. (1999), Math. Biosci. 191 (2004), 159-184.
3. J. Folkman, Tumor angiogenesis: therapeutic implications, N. Engl. J. Med. 285 (1971), 1182-1184.
4. P. Hahnfeldt, D. Panigrahy, J. Folkman, and Hlatky L., Tumor development under angiogenic signaling: a dynamic theory of tumor growth, treatment response, and postvascular dormancy, Cancer Res. 59 (1999), no. 4770.
5. R. Jain, Normalization of tumor vasculature: An emerging concept in antiangiogenic therapy, Science 307 (2005), no. 5706, 58-62.