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Optimal control for a class of compartmental models in cancer chemotherapy

Andrzej ŚwierniakUrszula LedzewiczHeinz Schättler — 2003

International Journal of Applied Mathematics and Computer Science

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 B and C, are...

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

Urszula LedzewiczVignon OussaHeinz Schättler — 2009

Applicationes Mathematicae

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 is minimized...

An optimal control approach to cancer treatment under immunological activity

Urszula LedzewiczMohammad NaghnaeianHeinz Schättler — 2011

Applicationes Mathematicae

Mathematical models for cancer treatment that include immunological activity are considered as an optimal control problem with an objective that is motivated by a separatrix of the uncontrolled system. For various growth models on the cancer cells the existence and optimality of singular controls is investigated. For a Gompertzian growth function a synthesis of controls that move the state into the region of attraction of a benign equilibrium point is developed.

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