The Dynamics of an Optimally Controlled Tumor Model: A Case Study
Mathematics (HMC), Mathematics (Pomona)
Cancer, Tumor, Population models, Competition models, Mathematical modelling, Immune system, Optimal control, Ordinary differential equations
We present a phase-space analysis of a mathematical model of tumor growth with an immune response and chemotherapy. We prove that all orbits are bounded and must converge to one of several possible equilibrium points. Therefore, the long-term behavior of an orbit is classified according to the basin of attraction in which it starts. The addition of a drug term to the system can move the solution trajectory into a desirable basin of attraction. We show that the solutions of the model with a time-varying drug term approach the solutions of the system without the drug once treatment has stopped. We present numerical experiments in which optimal control therapy is able to drive the system into a desirable basin of attraction, whereas traditional pulsed chemotherapy is not.
© 2003 Elsevier B.V.
L.G De Pillis, A Radunskaya, The dynamics of an optimally controlled tumor model: A case study, Mathematical and Computer Modelling, Volume 37, Issue 11, June 2003, Pages 1221-1244, ISSN 0895-7177, 10.1016/S0895-7177(03)00133-X. (http://www.sciencedirect.com/science/article/pii/S089571770300133X)