Concluding Remarks

Abstract

The question how therapeutic agents should be administered in order to maximize their potential effects is of fundamental importance in medical treatments. In the administration of cancer treatments, these questions are still far from being answered conclusively. In this text, we have explored what can be said about this topic from an analysis of minimally parameterized models described by ordinary differential equations using an optimal control approach. Clearly, more precise and in this sense more realistic models exist. These range from the inclusion of spatial aspects in partial differential equations to the incorporation of random features in stochastic models to complex agent-based models. Becoming increasingly more precise, such models, however, are prone to the pitfalls of Borges’s cartographers guild [33]. While current computer technologies enable large-scale computations and simulations, the number of parameters involved automatically carries with it uncertainty. Also, no matter how precise the data are that are available, the values of the parameters are for a particular case and numerical results pertain to a specific situation. On the other hand, the models considered here are all highly aggregated population based models, which, having small dimensions, allows to examine the underlying models analytically, not just numerically. Indeed, fairly robust qualitative features emerge from our analysis that we still would like to summarize.