V3I9P17

Optimal Control of a Reaction–Diffusion Tumor Growth Model

Ashraf Awadelkarim Suliman^1*

Abstract

This paper investigates the optimal control of tumor growth using a spatially distributed reaction-diffusion model. The control variable represents the administration of a cytotoxic drug, with the objective of minimizing both tumor burden and drug usage. We formulate a PDE-constrained optimal control problem, derive the necessary optimality conditions, and implement numerical simulations in MATLAB to illustrate tumor dynamics under optimal treatment strategies. Sensitivity analysis demonstrates the influence of key parameters, such as tumor proliferation rate, diffusion coefficient, and drug effectiveness, on the optimal dosing profile. The results provide valuable insights for designing patient-specific and spatially optimized cancer therapy protocols.

Keywords:

Optimal control, Reaction-diffusion PDE, Tumor growth, Cancer treatment, Numerical simulation, Drug administration, Sensitivity analysis