A two phase age dependent and two-mutation stochastic model of carcinogenesis

Abstract

An age dependent and two-mutation stochastic model of carcinogenesis is formulated and studied. In this model, we introduce a fitness age T, (a positive constant) for each cell to divide into two cells. A normal cell if its age is not greater than T either divides into two normal cells or divides into one normal cell and one intermediate cell or dies. A normal cell if its age is greater than T either divides into one normal cell and one intermediate cell, or divides into two intermediate cells or dies. An intermediate cell if its age is not greater than T divides into two intermediate cells or divides into one intermediate cell and one malignant cell or dies. An intermediate cell if its age is greater than T divides into one intermediate cell and one malignant cell or 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. It is shown that the production of malignant cells in one-mutation model is faster than that in two-mutation model. A numerical illustration is presented to highlight the performance of the model.