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2009, Volume 12, Issue 2: 415-438. Doi: 10.3934/dcdsb.2009.12.415
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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

  • 3.

    Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899

Received:  July 31, 2008
Revised:  March 31, 2009
Published:  August 2009
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: Primary: 49J15; Secondary: 93C50.

    Citation:
    shu

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