Catalog of the optimal controls in cancer chemotherapy for the Gompertz model depending on PK/PD and the integral constraint

Luis A. Fernández; Cecilia Pola

doi:10.3934/dcdsb.2014.19.1563

Article Contents

2014, Volume 19, Issue 6: 1563-1588. Doi: 10.3934/dcdsb.2014.19.1563

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Catalog of the optimal controls in cancer chemotherapy for the Gompertz model depending on PK/PD and the integral constraint

Luis A. Fernández^1, and
Cecilia Pola^1,

1.
Dep. Matemáticas, Estadística y Computación, Universidad de Cantabria, Avda. de los Castros, s/n, 39005 Santander

Received: July 31, 2013

Revised: January 31, 2014

Published: July 2014

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Abstract

We study three optimal control problems associated with Gompertz-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.

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Mathematics Subject Classification: 93C15, 49K15, 49M05, 49M37, 92C50.

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