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Ensemble Optimal Control for Managing Drug Resistance in Cancer Therapies.

Alessandro Scagliotti^1,2, Federico Scagliotti^3,4, Laura Deborah Locati^3,4

¹CIT School, Technical University of Munich, Boltzmannstr. 3/II, Garching bei München, 85748, Germany. scag@ma.tum.de.

Bulletin of Mathematical Biology

|May 21, 2026

Summary

This study introduces ensemble optimal control for cancer treatment, moving beyond maximal tolerated drug dose (MTD) to manage long-term disease. It proposes a new

Keywords:

Cancer modeling Drug resistance management Ensemble optimal control Gradient-based optimization

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Area of Science:

Mathematical Oncology
Control Theory
Computational Biology

Background:

Classical cancer treatment often uses maximal tolerated drug dose (MTD), which may not be optimal for managing competing sensitive and resistant cell populations.
Long-term cancer management is crucial when complete tumor eradication is not feasible.
Understanding tumor cell dynamics, including competition for resources, is key to developing advanced treatment strategies.

Purpose of the Study:

To apply ensemble optimal control for enhanced pharmacological cancer treatment strategies.
To develop methods for long-term disease management, particularly in cases where complete tumor eradication is not achievable.
To explore alternatives to the maximal tolerated drug dose (MTD) approach by considering tumor cell competition.

Main Methods:

Utilizing a Lotka-Volterra model to represent competing tumor cell subpopulations (sensitive and resistant).
Implementing an ensemble control framework to derive optimal treatment policies.
Performing numerical simulations for prostate cancer under androgen deprivation therapy.

Main Results:

Established general ensemble optimal control results applicable to various cancers.
Developed a treatment policy for prostate cancer that mimics the 'active surveillance' paradigm.
Identified limitations of the maximal tolerated drug dose (MTD) approach in exploiting cell competition.

Conclusions:

Ensemble optimal control offers a promising framework for advanced cancer treatment strategies.
The proposed 'Off-On' adaptive therapy (AT) variant, inspired by numerical findings, warrants further investigation.
Optimizing treatment by considering the dynamics of sensitive and resistant cell populations can lead to improved long-term disease management.