Conditional success of adaptive therapy: The role of treatment thresholds and non-existence of optimal strategies revealed by mathematical modelling and optimal control

¹ School of Mathematics Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China
² School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China
³ College of Science and Engineering, James Cook University, Queensland 4814, Australia
⁴ Western Sydney University, Sydney, Australia
⁵ Department of Liver Surgery, Peking Union Medical College Hospital, Chinese Academy of Medical Sciences & Peking Union Medical College, Beijing 100730, China

^* Corresponding authors: This email address is being protected from spambots. You need JavaScript enabled to view it. ; This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 21 February 2025
Accepted: 9 March 2026

Abstract

Adaptive therapy improves cancer treatment by controlling the competition between sensitive and resistant cells through treatment holidays. This study highlights the role of treatment-holidays and the treatment-restarting thresholds in adaptive therapy for tumours 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 thresholds for pausing and resuming treatment and on competitive interactions between cell populations. Three comparison scenarios between adaptive therapy and other therapies emerge, including uniform-decline where adaptive therapy underperforms regardless of threshold, conditional-improve where efficacy requires threshold optimisation, and uniform-improve where adaptive therapy consistently outperforms alternatives. Tumour initial conditions such as initial burden and initial resistant cell proportion influence 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 unrealisable as it requires infinitely many treatment holidays, rendering it clinically impractical. These findings emphasize personalised treatment strategies for enhancing long-term therapeutic outcomes.