CATALOG OF THE OPTIMAL CONTROLS IN CANCER CHEMOTHERAPY FOR THE GOMPERTZ MODEL DEPENDING ON PK/PD AND THE INTEGRAL CONSTRAINT

摘要

We study three optimal control problems associated with Gom-pertz-type differential equations, including bound control and integral constraints. These problems can be interpreted in terms of planning anticancer therapies. Existence of optimal controls is proved and all their possible structures are determined in detail, by using the Pontryagin's Maximum Principle. The influence of the pharmacokinetics and pharmacodynamics variants, together with the integral constraint, is analyzed. Moreover, the numerical results of some illustrative examples and our conclusions are presented.