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| In this talk, we will present delayed and ordinary differential equation models of periodic chemotherapy targeting solid tumors. Necessary and sufficient conditions for stability of the cancer free equilibrium are derived. The existence of numerically (and experimentally) observed periodic solutions is investigated using tools from functional analysis and floquet theory. A number of open problems regarding these results in a more general setting will be presented. We will also discuss the problem of parameter identifiability for some of our models. Finally, we will present a clinical application of the model, by applying it to the treatment of ovarian cancers with combination chemotherapy. The drugs considered include: platinum based compounds that induce cell death by inflicting DNA damage; taxols that target cells undergoing mitosis; and small molecule cell death inducers. The model is calibrated versus in vitro experimental results, and is then used to predict optimal doses and administration time scheduling for the treatment of a tumor growing in vivo. |
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