Analysis and Mean-Field Limit of a Hybrid PDE-ABM Modeling Angiogenesis-Regulated Resistance Evolution

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Abstract

Mathematical modeling is indispensable in oncology for unraveling the complex interplay between tumor growth, vascular remodeling, and therapeutic resistance. Here, we address the critical need for integrative frameworks capturing bidirectional feedback between hypoxia-driven angiogenesis and stochastic resistance evolution, an aspect often treated in isolation by previous continuum or agent-based models. We develop a novel hybrid partial differential equation–agent-based model (PDE-ABM) formulation unifying reaction-diffusion equations for oxygen, drug, and tumor angiogenic factor (TAF) with Gillespie-driven stochastic phenotype switching and discrete vessel-agent dynamics. Our work fills a methodological gap by providing the first rigorous well-posedness proof for this class of coupled systems, alongside detailed numerical analysis of discretization schemes and derivation of analytically tractable mean-field PDE limits via moment-closure techniques. The mean-field limit unifies the hybrid system into one PDE system, linking stochastic microdynamics with deterministic macrodynamics. By combining mathematical rigor with biologically interpretable outputs, our framework establishes a foundation for predictive multiscale oncology models and enables future data-driven therapeutic design.