# American Institute of Mathematical Sciences

September  2009, 12(2): 415-438. doi: 10.3934/dcdsb.2009.12.415

## Scheduling of angiogenic inhibitors for Gompertzian and logistic tumor growth models

 1 Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL 62026 2 Dept. of Mathematics and Computer Science, St. Louis University, St. Louis, MO 63103, United States 3 Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899

Received  August 2008 Revised  April 2009 Published  July 2009

The problem of scheduling a given amount of angiogenic inhibitors is considered as an optimal control problem with the objective of maximizing the achievable tumor reduction. For a dynamical model for the evolution of the carrying capacity of the vasculature formulated in [15] optimal controls are computed for both a Gompertzian and logistic model of tumor growth. While optimal controls for the Gompertzian model typically contain a segment along which the control is singular, for the logistic model optimal controls are bang-bang with at most two switchings.
Citation: Urszula Ledzewicz, James Munden, Heinz Schättler. Scheduling of angiogenic inhibitors for Gompertzian and logistic tumor growth models. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 415-438. doi: 10.3934/dcdsb.2009.12.415
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