Dynamics of a Data Based Ovarian Cancer Growth and Treatment Model with Time Delay

摘要

We present a simple model that describes ovarian tumor growth and tumor induced angiogenesis, subject to on and off anti-angiogenesis treatment. The tumor growth is governed by Droop's cell quota model, a mathematical expression developed in ecology. Here, the cell quota represents the intracellular concentration of necessary nutrients provided through blood supply. We present mathematical analysis of the model, including proving positivity of the solutions so that they are biologically meaningful, as well as discussing local and global stability. The mathematical model can be employed to fit both on-treatment and off-treatment preclinical data using the same biologically relevant parameters. We also state an open mathematical question.