The Role of Noise in Tumor–Immune Interactions: A Stochastic Simulation Study

In this article, we numerically investigate the effects of noise and heterogeneity on a model of immune–tumor cell interactions. We focus on stochastic dynamics and simulation-based analysis of the time required for tumor elimination. We identify the existence of a bistable response, which is disrupted by the introduction of intrinsic noise into the system. In particular, we characterize noise-induced transitions using first-passage time statistics and waiting-time distributions. We discuss various scenarios of tumor elimination, including the impact of vitamin intake and chemotherapy on tumor cell count, mean elimination time, and the duration of tumor dominance. Our results show that increasing chemotherapy reduces the maximum tumor count and decreases the average tumor elimination time, while intrinsic noise promotes memoryless switching toward the tumor-free state. This behavior is explained by the emergence of a quasi-stationary distribution governing the metastable tumor-present regime, leading to exponentially distributed extinction times. Furthermore, this framework enables the decay rate λ to be estimated from simulation data and related to treatment parameters (β1,γ). These findings provide a theoretical and statistical justification for memoryless tumor elimination dynamics and offer quantitative insights into stochastic treatment outcomes.