Title: Bistability and Noise-Induced Evasion in Tumor-Immune Dynamics with Antigen Accumulation and Immune Escape Show Chinese title

Title: 肿瘤-免疫动力学中的双稳态和噪声诱导的逃逸，具有抗原积累和免疫逃逸

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 bistability between immune surveillance and immune escape states, providing a mechanistic explanation for heterogeneous immune outcomes during tumor progression. 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 non-monotonic nature of tumor-immune dynamics. Show Chinese abstract

Abstract: 肿瘤-免疫相互作用由肿瘤微环境中的抗原异质性和随机扰动共同塑造，然而免疫相变的数学机制仍不明确。 我们提出一个包含抗原积累和免疫逃逸突变的四隔室动力学模型。 分岔分析揭示了免疫监视和免疫逃逸状态之间的双稳态，为肿瘤进展过程中不同的免疫结果提供了机制解释。 在多稳态区域，鞍点的稳定流形将状态空间划分为不同的吸引盆地，决定了系统的长期命运。 我们进一步分析了肿瘤微环境中的随机波动如何扰动这些分离曲线，可能触发不可逆的状态转换。 通过表征临界噪声强度并估计临界时间，我们建立了一个评估噪声诱导转换的数学框架。 该模型进一步预测，增加肿瘤细胞死亡可以提高系统对随机扰动的抵抗力，而更强的免疫压力可能促进免疫逃逸—突显了肿瘤-免疫动力学的非线性和非单调特性。