A two-mutation model of carcinogenesis which evolves under the influence of three level random environment on the production process is formulated and analyzed. A random environment occupies one of the levels 1, 2 and 3 at any time t according to a Markov process. 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 one normal cell and one intermediate cell or dies and an intermediate cell either divides into one intermediate cell and one malignant cell or dies. When the environment is in level 3, a normal cell either divides into two intermediate cells or dies and an intermediate cell either divides into two malignant 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 at any time t. KeywordsAge-dependent two-stage stochastic model, Normal cell, Intermediate cell, Malignant cell, Random environment.

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三级环境过程驱动的致癌作用的两阶段突变随机模型

建立并分析了在三级随机环境对生产过程的影响下演化的致癌物的两个突变模型。根据马尔可夫过程，随机环境在任何时间t都占据级别1，级别2和级别3之一。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，正常细胞要么分为一个正常细胞和一个中间细胞或死亡，一个中间细胞要么分为一个中间细胞和一个恶性细胞或死亡。当环境处于第3级时，正常细胞要么分为两个中间细胞或死亡，一个中间细胞要么分为两个恶性细胞或死亡。假设，一旦产生了恶性细胞，它就会以1的概率产生恶性肿瘤。我们可以在任何时间t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