Abstract Metastasis, the spread of cancer cells from a primary tumor to secondary location(s) in the human organism, is the ultimate cause of death for the majority of cancer patients. Although studied for more than 180 years, increasing efforts in recent years have significantly contributed to a better understanding of this aspect of tumor development. Adding to this understanding, our current paper proposes a multi-type branching process model, through which various topics, such as extinction of cancer cell clones, occurrence of successful mutants, and immediate risk of escaping extinction, are investigated. More specifically, the relationship between the lifespan distribution of cancer cells with subcritical reproduction and the waiting time until the occurrence of a mutant (having supercritical reproduction) cancer cell, escaping extinction, is highlighted. The theoretical studies formulated in this paper may allow our model to be tailored to real data available for particular kinds of cancer and chemotherapy.

中文翻译：

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多类型年龄依赖性分支过程作为转移进化模型

摘要 转移，即癌细胞从原发肿瘤扩散到人体组织中的继发部位，是大多数癌症患者死亡的最终原因。尽管研究了 180 多年，但近年来不断增加的努力大大有助于更好地了解肿瘤发展的这一方面。除了这种理解之外，我们当前的论文提出了一种多类型分支过程模型，通过该模型研究了各种主题，例如癌细胞克隆的灭绝、成功突变的发生以及逃避灭绝的直接风险。更具体地说，具有亚临界繁殖的癌细胞的寿命分布与直到发生突变（具有超临界繁殖）癌细胞，逃脱灭绝的等待时间之间的关系，突出显示。本文中阐述的理论研究可能使我们的模型能够根据可用于特定类型癌症和化疗的真实数据进行定制。