title: Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls.
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.
authors.affiliation: Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, United States. depillis@hmc.edu
authors.forename: L G
authors.initials: LG
authors.lastname: de Pillis
authors.forename: W
authors.initials: W
authors.lastname: Gu
authors.forename: K R
authors.initials: KR
authors.lastname: Fister
authors.forename: T
authors.initials: T
authors.lastname: Head
authors.forename: K
authors.initials: K
authors.lastname: Maples
authors.forename: A
authors.initials: A
authors.lastname: Murugan
authors.forename: T
authors.initials: T
authors.lastname: Neal
authors.forename: K
authors.initials: K
authors.lastname: Yoshida
mesh_terms: D000970:Antineoplastic Agents / Q000627:therapeutic use*; D048708:Cell Growth Processes / Q000187:drug effects / Q000502:physiology; D003198:Computer Simulation; D006801:Humans; D016014:Linear Models; D008954:Models, Biological; D009369:Neoplasms / Q000188:drug therapy* / Q000276:immunology* / Q000473:pathology
chemical_list: D000970:Antineoplastic Agents