Bistability and Noise-Induced Evasion in Tumor-Immune Dynamics with Antigen Accumulation and Immune Escape

Abstract

Abstract. Tumor-immune interactions are shaped by both antigenic heterogeneity and stochastic perturbations in the tumor microenvironment, yet the mathematical mechanisms underlying immune phase transitions remain poorly understood. We propose a four-compartment dynamical model that incorporates antigen accumulation and immune escape mutations. Bifurcation analysis reveals how the coupling of antigenic evolution and escape mechanisms dictates system bistability, providing a mechanistic explanation for heterogeneous immune outcomes during tumor progression. We identify a double-edged sword effect where elevated mutation rates facilitate both immune recognition and clonal escape. In the multistable regime, the stable manifold of a saddle point partitions the state space into distinct basins of attraction, determining the long-term fate of the system. We further analyze how stochastic fluctuations in the tumor microenvironment perturb these separatrices, potentially triggering irreversible state transitions. By characterizing the critical noise intensity and estimating the tipping time, we establish a mathematical framework for assessing noise-induced transitions. The model further predicts that increasing tumor cell death can improve system resilience to stochastic perturbations, whereas stronger immune pressure may facilitate immune escape—highlighting the nonlinear and nonmonotonic nature of tumor-immune dynamics.