Conditional Success of Adaptive Therapy: The Role of Treatment-Holiday Thresholds and Non-Existence of Optimal Strategies Revealed by Mathematical Modelling and Optimal Control

Abstract

Adaptive therapy improves cancer treatment by controlling the competition between sensitive and resistant cells through treatment holidays. This study highlights the critical role of treatmentholiday thresholds in adaptive therapy for tumors composed of drug-sensitive and resistant cells. Using a Lotka-Volterra model, adaptive therapy outcomes are compared with maximum tolerated dose therapy and intermittent therapy outcomes, showing that adaptive therapy success depends critically on the threshold for pausing and resuming treatment and on competitive interactions between cell populations. Three comparison scenarios between adaptive therapy and other therapies emerge: uniform-decline where adaptive therapy underperforms regardless of threshold, conditional-improve where efficacy requires threshold optimization, and uniform-improve where adaptive therapy consistently outperforms alternatives. Tumor composition including initial burden and resistant cell proportion influences outcomes. Threshold adjustments enable adaptive therapy to suppress resistant subclones while preserving sensitive cells, extending progression-free survival. Crucially, this work establishes an optimal control problem for time-to-progression and mathematically proves that under biological constraints like neutral competition or low initial burden, the theoretically optimal strategy is unrealizable as it requires infinitely many treatment holidays, rendering it clinically impractical. These findings emphasize personalized treatment strategies for enhancing long-term therapeutic outcomes. Mathematics Subject Classification92C50,92C42.