Optimal Control in Chemotherapy of Cancer

Werner Krabs and Stefan Pickl ()
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Werner Krabs: Technical University of Darmstadt, Department of Mathematics
Stefan Pickl: Universität der Bundeswehr München, Department of Computer Science

Chapter 5 in Dynamical Systems, 2010, pp 217-230 from Springer

Abstract: Abstract We describe the time dependent size of the tumor by a real valued function $$ T = T (t), \,\, t \in {\mathbb R}$$ (t denotes the time), which we assume to be differentiable. The temporal development of this size (without treatment) we assume to be governed by the differential equation $$ \dot{T}(t)= f(T(t))T(t), \quad t \in {\mathbb R}, $$ where the function $$ f : {\mathbb R}_+ \rightarrow {\mathbb R}_+ $$ is the growth rate of the tumor which is assumed to be in $$C^1 ({\mathbb R}_+)$$ and to satisfy the condition $$ f\prime(T)

Date: 2010
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DOI: 10.1007/978-3-642-13722-8_5

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