Optimal control problem for a general reaction-diffusion tumor-immune system with chemotherapy

An optimal control problem of a general reaction-diffusion tumor-immune system with chemotherapy is investigated to minimize the tumor burden and side effects as well as treatment costs. Firstly, the existence, uniqueness and some estimates of strong solution to the state system in spatial dimensions n = 1 , 2, 3 are obtained by making use of the semigroup theory and truncation method. Subsequently, we prove the existence of optimal pair by utilizing the minimizing sequence technique. Furthermore, we show the differentiability of the control-to-state mapping and establish the first-order necessary optimality condition. Finally, several numerical simulations are presented to illustrate the practical application of the theoretical results obtained in this work and to validate some clinical observations. (C) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

The study examines an optimal control problem for a general reaction-diffusion tumor-immune system with chemotherapy to minimize tumor burden and treatment costs. Theoretical analysis reveals the optimal treatment strategy, and numerical simulations demonstrate its potential value in clinical applications.