Drug resistance and phase specificity of cancer chemotherapy-finite versus infinite dimensional models

In this paper we combine models that so far have been studied separately, taking into account both the phenomenon of gene amplification and drug specificity in chemotherapy, in their different aspects. The finite dimensional model into account only two levels of drug resistance but it allows for rigorous mathematical analysis. 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. We compare both approaches and present our results dealing with optimization of protocols based on optimal control problems formulated for them. The optimal control problem is defined in 1 ¹ space.