Displaying similar documents to “An optimal control approach to cancer treatment under immunological activity”

Optimal solutions for a model of tumor anti-angiogenesis with a penalty on the cost of treatment

Urszula Ledzewicz, Vignon Oussa, Heinz Schättler (2009)

Applicationes Mathematicae

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The scheduling of angiogenic inhibitors to control a vascularized tumor is analyzed as an optimal control problem for a mathematical model that was developed and biologically validated by Hahnfeldt et al. [Cancer Res. 59 (1999)]. Two formulations of the problem are considered. In the first one the primary tumor volume is minimized for a given amount of angiogenic inhibitors to be administered, while a balance between tumor reduction and the total amount of angiogenic inhibitors given...

Optimal Control of a Cancer Cell Model with Delay

C. Collins, K.R. Fister, M. Williams (2010)

Mathematical Modelling of Natural Phenomena

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In this paper, we look at a model depicting the relationship of cancer cells in different development stages with immune cells and a cell cycle specific chemotherapy drug. The model includes a constant delay in the mitotic phase. By applying optimal control theory, we seek to minimize the cost associated with the chemotherapy drug and to minimize the number of tumor cells. Global existence of a solution has been shown for this model and ...

Delay Dynamics of Cancer and Immune Cell Model

D. Adongo, K.R. Fister (2012)

Mathematical Modelling of Natural Phenomena

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We investigate optimal control of a cancer-immune cell interactive model with delay in the interphase compartment. By applying the optimal control theory, we seek to minimize the cost associated with the chemotherapy drug, minimize the accumulation of cancer cells, and increase the immune cell presence. Optimality conditions and characterization of the control are provided. Numerical analyses are given to enhance the understanding of the ...

Optimal control for a class of compartmental models in cancer chemotherapy

Andrzej Świerniak, Urszula Ledzewicz, Heinz Schättler (2003)

International Journal of Applied Mathematics and Computer Science

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We consider a general class of mathematical models P for cancer chemotherapy described as optimal control problems over a fixed horizon with dynamics given by a bilinear system and an objective which is linear in the control. Several two- and three-compartment models considered earlier fall into this class. While a killing agent which is active during cell division constitutes the only control considered in the two-compartment model, Model A, also two three-compartment models, Models...