Steering the Evolutionary Game: Hierarchical Control of Therapeutic Resistance in Cancer Treatment

Arvid E. Gollwitzer, Deepak A. Subramanian, Isaac Tucker, Giovanni Traverso

Additional Submission Instructions: For the camera-ready version, please include the author names and affiliations, funding disclosures, and acknowledgements.

Track: Track 1: Original Research/Position/Education/Attention Track

Keywords: Mathematical Oncology, Therapeutic Resistance, Eco-evolutionary Dynamics, Evolutionary Game Theory, Hierarchical Control, Singular Perturbation Theory, Microbiome Modulation, Fitness Landscape Engineering

TL;DR: A hierarchical game-theoretic framework that recasts cancer therapy from dynamic evolutionary tracking to static fitness landscape engineering, guaranteeing global stability of the tumor-free state and robustly mitigating therapeutic resistance.

Abstract:

Therapeutic failure in cancer often arises from Darwinian selection for drug resistance. We introduce a hierarchical ecological control framework that reshapes the evolutionary fitness landscape on a slow timescale (microbiome modulation) to render the fast tumor-immune-drug dynamics curative. We prove existence and uniqueness of a Markov-perfect Nash equilibrium for the LQ fast game and formalize a conservative robust immune-influx threshold $s_{crit,\\max}^{rob}\\!\\le\\!\\tfrac{d}{n}a$. All nonlinear results are stated relative to $s_{crit,\\max}^{rob}$. Maintaining $s(\\mathbf M)\\!\\ge\\!s_{crit,\\max}^{rob}+\\delta$ renders the tumor-free state globally exponentially stable with rate $\\lambda=\\min\\{\\tfrac{n\\delta}{2d},\\,\\tfrac{d-g_{\\max}}{2}\\}$ and explicit gain bounds. Robustness is established via: (i) spatial sufficiency using domain eigenvalues precluding sanctuaries, (ii) global asymptotic stability in probability under stochastic perturbations when $L_z<\\sqrt{\\lambda/K}$ (and almost-sure convergence under additional recurrence conditions), (iii) quantitative tolerance to clonal heterogeneity when $\\Delta_a+\\Delta_\\kappa u_{d,\\max}<\\tfrac{n}{d}\\,\\delta$, (iv) delay and observer robustness under precise small-gain and observability conditions, and (v) an $\\epsilon$-accurate Fenichel decomposition of the two-timescale game.

Using TCGA-derived priors, AI-synthesized policies enforce the stability margin along trajectories and achieve high efficacy with lower cytotoxic exposure. In Skin Cutaneous Melanoma (SKCM) the controller achieves **89%** eradication (95% CI $\\pm 6$), maintains time-above-threshold at **92%** ($\\pm 5$), and reduces peak tumor burden by **57%**; first response occurs in 28-35 days with a lower dose index. In colorectal cancer (CRC) the controller achieves **76%** eradication ($\\pm 7$) with **88%** time-above-threshold ($\\pm 6$). Across structured perturbations (5-clone heterogeneity, 14-day delay, stochastic noise, partial observability), individual eradication rates exceed 80% and remain 73% under combined stressors, aligning with the theory. These results establish ecological landscape engineering as a principled, general strategy for mitigating resistance in oncology.

Submission Number: 356