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Dynamics of tumor-immune interaction under treatment as an optimal control problem

Pages: 971 - 980, Issue Special, September 2011

 Abstract        Full Text (304.2K)              

Urszula Ledzewicz - Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL 62026, United States (email)
Mohammad Naghnaeian - Dept. of Mechanical Science and Engineering, Univeristy of Illinois at Urbana-Champaign, 1206 W. Green Street, Urbana, IL, 61801-2906, United States (email)
Heinz Sch├Ąttler - Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899, United States (email)

Abstract: For a mathematical model for cancer-immune system interactions under chemotherapy, we consider the problem of moving an initial condition that lies in a region of malignant cancer growth through therapy into a region where cancer regresses and thus control the cancer. We formulate this treatment goal as an optimal control problem and discuss the solutions for various related objective functions in the model.

Keywords:  optimal control, cancer chemotherapy, tumor-immune interaction
Mathematics Subject Classification:  Primary: 49K15; Secondary: 92C50

Received: July 2010;      Revised: August 2010;      Published: October 2011.