On the Role of the Objective in the Optimization of Compartmental Models for Biomedical Therapies

In the talk we review and discuss results obtained through an application of tools of nonlinear optimal control to biomedical problems. We start with introducing a general form of the compartmental model and then discuss various aspects of its dynamics (such as growth and interaction terms), modeling of treatment (including pharmacometrics of the drugs), and give special attention to the choice of the objective functional which represents the goal of the treatment. Indeed, many properties of optimal solution are predestined by this choice which often is only made casually using some simple ad-hoc heuristics. Using the examples from our own research and work encountered in the literature we will discuss pitfalls and dangers in choosing the objectives in biomedical problems. We will give suggestions how to improve this choice by taking into account the underlying biology of the problem. The "take home message" from the talk is that although there is not such a thing as the one and only right choice of the objective for the problem, there are many wrong ones.