On a multiobjective optimal control of a tumor growth model with immune response and drug therapies

In this paper, we consider a tumor growth mathematical model that includes an immune system and drug therapies. Immuno- and chemodrug administration as well as periodic administration of radiation are integrated in the model. We have set an optimal control (OC) problem relative to the model so that the average number of tumor cells and immuno- and chemotherapeutic drug administration are simultaneously minimized in a multiobjective context. The external injection of two immunostimulators and a chemotherapeutic drug has been considered as control, and the objective functionals aim to reflect the severity of both types of drug administration. The multiobjective approach to the OC of the tumor growth model provides good-quality approximate solutions and has shown to be a valuable procedure to identify good trade-offs between conflicting objectives.The authors wish to thank an anonymous referee and the Associate Editor for their valuable comments and suggestions to improve the paper. This work has been supported by COMPETE (POCI-01-0145-FEDER-007043) and FCT - Fundacao para a Ciencia e Tecnologia within the projects UID/CEC/00319/2013 and UID/MAT/00013/2013.