Chemotherapy for Tumors: An Analysis of the Dynamics and a Study of Quadratic and Linear Optimal Controls

Authors

Lisette G. de Pillis, Harvey Mudd CollegeFollow
Weiqing Gu, Harvey Mudd CollegeFollow
K Renee Fister, Murray State University
Tiffany Head '06, Harvey Mudd CollegeFollow
Kenny Maples '06, Harvey Mudd CollegeFollow
Anand Murugan, Pomona College
Todd Neal, Murray State University
Kenji Yoshida '08, Harvey Mudd CollegeFollow

Student Co-author

HMC Undergraduate, Pomona Undergraduate

Document Type

Article

Department

Mathematics (HMC)

Publication Date

9-2007

Abstract

We investigate a mathematical model of tumor–immune interactions with chemotherapy, and strategies for optimally administering treatment. In this paper we analyze the dynamics of this model, characterize the optimal controls related to drug therapy, and discuss numerical results of the optimal strategies. The form of the model allows us to test and compare various optimal control strategies, including a quadratic control, a linear control, and a state-constraint. We establish the existence of the optimal control, and solve for the control in both the quadratic and linear case. In the linear control case, we show that we cannot rule out the possibility of a singular control. An interesting aspect of this paper is that we provide a graphical representation of regions on which the singular control is optimal.

Rights Information

© 2007 Elsevier

DOI

10.1016/j.mbs.2006.05.003

Recommended Citation

L.G. de Pillis, K. Renee Fister, Weiqing Gu, Kenny Maples, Tiffany Head, Todd Neal, Kenji Yoshida, Anand Murugan, "Chemotherapy for Tumors: An Analysis of the Dynamics and a Study of Quadratic and Linear Optimal Controls", Mathematical Biosciences, Vol 209, 2007, pp. 292-315.