`Computational and Mathematical Methods in MedicineVolume 9 (2008), Issue 1, Pages 1-26doi:10.1080/17486700701776447`
Original Article

## Evidence that Natural Immunity to Breast Cancer and Prostate Cancer Exists in the Majority of Their Risk Populations Is Predicted by a Novel, Inherently Saturated, Ordered Mutation Model

Physics Department, University of Maryland Baltimore County, 1000 Hilltop Circle, Catonsville, MD 21250, USA

Received 13 March 2007; Revised 27 September 2007; Accepted 25 October 2007

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The series of ordered mutations that cause a specific cell to become cancerous is modeled so that the fraction of a risk population (e.g. White men) that has developed a specific cancer (e.g. melanoma) at any age can be calculated. The saturated model constructed and solved here is isomorphic to the physical model describing an ordered chain of radioactive nuclei decays with the exception that it allows for the possibility that a fraction of a risk population may be immune to developing a specific cancer.

The simplest model developed here depends on only three independent parameters: the number of ordered mutations necessary for a cell to become cancerous, the fraction of the risk population that is immune to developing a specific cancer and the average time between mutations (a time defined as the mutation lifetime). The values of these independent parameters are determined by fitting the model's cancer incidence function to the cancer incidence data.

This model was applied to five widely different cancers: melanoma, pancreatic cancer, female breast cancer, non-Hodgkin lymphoma and prostate cancer. The modeling predicts that all White males in the USA are vulnerable to developing melanoma, five-ordered mutations are required to develop it and the mutation lifetime is 48.3 years. By contrast, the modeling predicts that 80.7% of White females in the USA are immune to developing melanoma, three-ordered mutations are required to develop it and the mutation lifetime is 78.9 years. Remarkably, it was also found that about 70% of females are immune to developing breast cancer and about 70% of males are immune to developing prostate cancer, predictions that fit in with the experimental evidence of cancer immunosurveillance and immunoediting.

Clearly, different risk populations can develop the same cancer through different pathways. Delineating the mechanism underlying the prevalence of immunity to specific cancers in specific risk populations should become a research priority. Finding ways of blocking or repairing cellular mutations and/or destroying mutated, potentially cancerous cells would prevent cancers from developing altogether and eliminate a major cause of mortality.