Control problems arising in cancer chemotherapy under evolving drug resistance - finite versus infinite dimensional models

This paper presents comparison of two classes of systems used in modelling of cancer chemotherapy. They combine models that so far have been studied separately, taking into account both the phenomenon of gene amplification and cycle specificity in chemotherapy, in their different aspects. The methodology of analysis of such models, based on system decomposition, is discussed. In the infinite dimensional model, the mathematical description is given by an infinite number of state equations with a system matrix, which form allows decomposing the model into two interacting subsystems. While the first one, of finite dimension, can have any form, the second one is infinite dimensional and tridiagonal. The finite dimensional model on the other hand takes into account only two levels of drug resistance but it allows for more rigorous mathematical analysis. The optimal control problem is defined in l¹ space.