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Carcinogenesis Models With Erlang Distributed Cell Life Lengths

Qi Zheng
Organization: Texas A&M University Health Science Center
Department: Department of Epidemiology and Biostatistics
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Mathematical modeling of the carcinogenesis process plays an important role in quantitative cancer research. Based on the classic MVK two-stage model, the author has proposed a model with Erlang distributed cell life lengths for the initiated cells ("On the MVK Stochastic Carcinogenesis Models With Erlang Distributed Cell Life Lenghts", Risk Analysis, August 1995 issue).

The package CarcinoErlang.m provides six functions to facilitate the numerical investiation reported in the paper (the original MVK model is also included in the package as a special case). The package enables the user to compute and plot the survival function and the mean value functions for both the initiated and malignant cells, when the model parameters (cell birth and death rates, etc.) are constants. The package also offers a function for computing the survival function of the MVK model whose parameters are piecewise constants. In addition to reproducing most of the numerical examples in the paper, the accompanying notebook CarcinoErlang.nb plots a survival function of an MVK model of piecewise constant parameters with the time interval partitioned into five subintervals.

*Mathematics > Probability and Statistics
*Science > Biology

carcinogenesis model, cancer, survival function, Erlang distribution
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CarcinoErlang.m (7.1 KB) - Mathematica Package
CarcinoErlang.nb (70.3 KB) - Example notebook for CarcinoErlang.m

Files specific to Mathematica 2.2 version:
CarcinoErlang.ma (65 KB) - Example notebook for CarcinoErlang.m