Optimal control strategies for the continuum model of pre-synthetic stage breast cancer tumor-immune interaction

Abstract

Abstract We present a continuum model to analyze optimal control strategies for breast tumor-immune interactions during the pre-synthetic stage. Motivated by the importance of early detection in cancer management, the model incorporates external immunotherapeutic stimulations targeting NK cells, Interferon-gamma, and Interleukin-2. We establish global well-posedness of strong solutions using C 0 -semigroup theory and prove the existence of optimal controls via a minimizing sequence approach. First-order optimality conditions are derived, and numerical simulations validate the theoretical results, showing tumor eradication under optimal immunotherapy. The spatial heterogeneity and wave-like tumor dynamics suggest localized immune activation and diffusion-driven suppression zones. This work provides both theoretical and computational insights that align with existing literature and highlight the potential of early-stage immune-based interventions.