Modeling of Tumor Growth and its Control via Paclitaxel Using a Delay Differential Equation
Paclitaxel is shown to be antiangiogenic at low doses, but the extent of these effects is not known. A mathematical model that describes tumor growth and response to treatment with a continuous, low dose treatment of the anti-mitotic drug Paclitaxel is considered. The model considers 3 populations: system cells, proliferating tumor cells, and tumor cells in a resting phase. A time delay accounts for the time it takes for tumor cells to complete one cycle in the proliferation phase. The system is first analyzed without drug administration, and then analyzed numerically under different levels of drug administration. We provide a rigorous analysis of a three dimensional differential equation system with a single delay. Finally, sensitivity analysis is performed on certain parameters to determine what the likely consequences of antiangiogenic effects.
Yi Lin, Emory University
Kevin Flores, University of California, Santa Barbara
Lauren Hannah, Princeton Univeristy