Article ID Journal Published Year Pages File Type
4500333 Mathematical Biosciences 2011 9 Pages PDF
Abstract

In this paper, two cancer therapies are investigated through their mathematical models. Namely, angiogenesis inhibition (P. Hahndfeldt, D. Panigrahy, J. Folkman, L. Hlatky, Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy, Cancer Res. 59, 1999, 4770–4775) and tumor-immune interactions with chemotherapy (L. De Pillis, W. Gu, K.R. Fister, T. Head, K. Maples, A. Murugan, T. Neal, K. Yoshida, Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls. Math. Biosci. 209 (1), 2007, 292–315). The feedback protocols are determined by using a control set-valued method whose mathematical foundations are stated in (K. Kassara, A unified set-valued approach to control immunotherapy, SIAM J. Contr. Optim. 48 (2), 2009, 909–924), and which is demonstrated to be well suited for cancer control.

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