Probability distribution of the number of initiated cells of carcinogenesis under prevention

In this paper, I have shown that under some mild conditions, the number of initiated cells in an extended two-stage model of carcinogenesis can be approximated by a diffusion process. By using this approximation, I have derived the probability distribution for the number of initiated cells in terms of Laguerre polynomials under normal prevention conditions. This follows from the fact that many of the dietary components are antioxidants which would neutralize the hydroxyl free radicals and hence, reduce the proliferation rates of initiated cells to interrupt or slow down the promotion stage in carcinogenesis.