Harsh Jain
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MATHEMATICS COLLOQUIUM
Speaker: Harsh Jain Abstract. In this talk, we will present ordinary differential equation models of chemotherapy targeting solid tumors. The drugs considered include: platinum based compounds that induce cell death by inflicting DNA damage; and taxols that target cells undergoing mitosis. Although such models are relatively simple in formulation, it is still not clear whether model parameters are identifiable from available experimental data. Here, we show that while nonlinearities in model terms generally result in structural identifiability, the increased numbers of parameters lead to issues of practical identifiability (due to imperfect or incomplete data). We discuss methods to estimate practically identifiable combinations of parameters in such cases. An important result of our analysis is predicting what sort of additional experimental data would render the model completely identifiable. Time permitting, we will also derive necessary and sufficient conditions for stability of the cancer free equilibrium, as well as investigate the existence of periodic solutions (corresponding to the periodic application of therapy), using tools from Floquet theory and functional analysis. |