A Two-Stage Mutation Stochastic Model of Carcinogenesis Driven by a Three Level Environmental Process

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.