In this paper, we present a two-stage stochastic model of carcinogenesis in a two level random environment. The random environment switches between two levels, say, 1 and 2 alternately. When the environment is in level 1, a normal cell either divides into two normal cells or dies; and an intermediate cell divides into two intermediate cells or dies. When the environment is in level 2, a normal cell either divides into two intermediate cells or divides into one normal cell and one intermediate cell or divides into two normal cells or dies; and an intermediate cell either divides into two malignant cells or divides into one intermediate cell and one malignant cell or divides into two intermediate cells or dies. It is assumed that, once a malignant cell is produced, it generates a malignant tumor with probability 1. We obtain the mean numbers of normal, intermediate and malignant cells. KeywordsAge-dependent two-stage stochastic model, Normal cell, Intermediate cell, Malignant cell, Random environment.

中文翻译：

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两级随机环境驱动的致癌作用的两阶段突变随机模型

在本文中，我们提出了在两级随机环境中的两阶段随机致癌模型。随机环境交替在两个级别（例如1和2）之间切换。当环境处于1级时，一个正常的细胞要么分成两个正常的细胞，要么死亡。中间单元分为两个中间单元或裸片。当环境处于第2级时，正常细胞要么分成两个中间细胞，要么分成一个正常细胞，一个中间细胞或者分成两个正常细胞或死亡。中间细胞或者分为两个恶性细胞，或者分为一个中间细胞和一个恶性细胞，或者分为两个中间细胞或死亡。假定一旦产生了恶性细胞，它就会以1的概率产生恶性肿瘤。我们获得正常，中度和恶性细胞的平均数。年龄相关的两阶段随机模型正常细胞中级细胞恶性细胞随机环境