Optimization of Cytostatic Leukemia Therapy in an Advection–Reaction–Diffusion Model

Abstract

In this work, we study an advection-reaction-diffusion system involving normal and cancer hematopoietic cells (HC) and modeling the development of leukemia in the bone marrow. The effects of a targeted cytostatic therapy, which inhibits the regeneration of cancer HC, are studied through an optimal control system. We prove the existence of a positive bounded solution and the existence of an optimal controls by semigroup techniques. Conditions of optimality are in terms of the dual system. The effects of targeted cytostatic therapy, upon the dynamics of normal and cancer HC, are discussed through numerical simulations.

Optimal Buffer Zone for the Control of Groundwater Pollution from Agricultural Activities

“…The better regularity of c * , compared to the one stated in Proposition 3, comes obviously from the additional assumptions of the present subsection 6. The terminology 'dual problem' is the one used in Benosman et al[30] and Barbu and Iannelli[31].…”

“…Since the existence and the uniqueness of the optimal solution have been proved in Proposition 3, the optimal solution may be characterised by the first order necessary optimality conditions. They are presented in the following lemma (proved in Subsection 5.3 using the Lagrangian of the problem as in Benosman et al [30]).…”

Optimal medication for tumors modeled by a Cahn–Hilliard–Brinkman equation

“…Due to the Sobolev embeddings H 1 ⊂ L p , H 1 ⊂ L p , p ∈ [1,6], and the boundedness of ϕ u ∈ L ∞ (H 1 ), we obtain…”

“…Results on optimal control problems for tumor models based on ODEs are investigated in [33,35,37,43]. In the context of PDE-based control problems we refer to [6] where a tumor growth model of advection-reaction-diffusion type is considered. There are various papers analyzing optimal control problems for Cahn-Hilliard equations (e.g., [10,30,42]).…”

Optimal Control for a Groundwater Pollution Ruled by a Convection–Diffusion–Reaction Problem

“…In a different context, Benosman et al [11] study the existence of an optimal control for an advection reaction diffusion model of leukemia therapy. Let us emphasize that our work differs from [11] (and thus extends their results) for several reasons. Firstly, our results are not restricted to one-dimensional in space models.…”