标题： 具有移动灭绝阈值的癌症模型再现了真实的癌症数据 显示英文标题

标题： Cancer model with moving extinction threshold reproduces real cancer data

摘要： 我们提出了一种简单的癌症发展动态模型，该模型能够捕捉癌变和随后的癌症进展。 模型的核心思想是将免疫系统纳入为灭绝阈值，类似于种群生物学中的强阿利效应。 我们首先识别了常用的阿利效应模型在再现典型癌症进展方面的局限性。 然后，我们通过推导一个新模型来解决这些局限性，该模型包括：(i) 干细胞随年龄增长而增加的随机突变率，以及 (ii) 免疫反应，其强度也可能随时间变化。 我们的模型准确地再现了广泛的现实世界癌症数据：大多数人类癌症的典型年龄特异性累积风险，小鼠乳腺癌的进展，以及女性乳腺癌的异常年龄特异性累积风险。 在最后一种情况下，我们使用移动灭绝阈值来反映月经周期不同阶段和更年期治疗的不同免疫反应。 这为我们提供了关于激素替代疗法和月经周期长度影响的新见解。 这种移动阈值方法可以应用于许多其他癌症场景，其中免疫反应或其他重要因素可能随时间变化。 显示英文摘要

摘要： We propose a simple dynamic model of cancer development that captures carcinogenesis and subsequent cancer progression. A central idea of the model is to include the immune system as an extinction threshold, similar to the strong Allee effect in population biology. We first identify the limitations of commonly used Allee effect models in reproducing typical cancer progression. We then address these limitations by deriving a new model that incorporates: (i) random mutations of stem cells at a rate that increases with age and (ii) immune response whose strength may also vary over time. Our model accurately reproduces a wide range of real-world cancer data: the typical age-specific cumulative risk of most human cancers, the progression of breast cancer in mice, and the unusual age-specific cumulative risk of breast cancer in women. In the last case, we use a moving extinction threshold to reflect the different immune response at different phases of the menstrual cycle and menopausal treatment. This provides new insights into the effects of hormone replacement therapy and menstrual cycle length. This moving threshold approach can be applied to a variety of other cancer scenarios where the immune response or other important factors may vary over time.