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 antimitotic drug Paclitaxel is considered. The model considers three populations: system cells, proliferating tumor cells, and tumor cells in a resting phase. A delay differential equation model 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. Finally, sensitivity analysis is performed on certain parameters to determine what the likely consequences of antiangiogenic effects.