The influence of fixed and free final time of treatment on optimal chemotherapeutic protocols

Abstract

Some general setups of optimal control problems purporting to design optimal noncycle specific drug regimens are analyzed within the frame of free final time. Maximum drug concentration or injection is actually the sole optimal strategy, whenever an optimal solution exists. This result seems to be strongly linked to the characteristic of free final time assumed in this work. In the context of fixed final time, it is shown in the works of Świerniak and Świerniak and Duda that singular control is the optimal drug regimen in the case of exponential cell growth, for instance. Moreover, there can exist qualitative as well as quantitative differences between the two setups in treatment duration and performance indices. These markedly differing outcomes point out the necessity of clearly defining the time boundary conditions in theoretical settings in the light of clinically accepted protocols.