Optimal control problems for a parabolic system modeling glioma therapy

TL;DR

This paper establishes the mathematical foundation for optimal control of a parabolic system modeling glioma therapy with oncolytic viruses, proving well-posedness, existence of optimal controls, and deriving necessary optimality conditions.

Contribution

It provides the first rigorous analysis of optimal control problems for a glioma therapy model based on oncolytic viruses, including well-posedness and optimality conditions.

Findings

Proved global in time well-posedness of the control model

Established existence of optimal controls for relevant objective functionals

Derived necessary conditions for optimality in the control problem

Abstract

In this paper we consider optimal control problems for a parabolic system modeling a therapy, based on oncolytic viruses, for the glioma brain cancer. Using several techniques typical of functional analysis, we prove the global in time well posedness of the control model, the existence of optimal controls for specific objective functionals, which are natural for cancer therapies, and we derive necessary conditions for optimality.