Math. Model. Nat. Phenom.
Volume 5, Number 3, 2010Mathematical modeling in the medical sciences
|Page(s)||134 - 164|
|Published online||28 April 2010|
Widespread Immunity to Breast and Prostate Cancers is Predicted by a Novel Model that also Determines Sporadic and Hereditary Susceptible Population Sizes
Physics Department, University of Maryland Baltimore County
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Natural immunity to breast and prostate cancers is predicted by a novel, saturated ordered mutation model fitted to USA (SEER) incidence data, a prediction consistent with the latest ideas in immunosurveillance. For example, the prevalence of natural immunity to breast cancer in the white female risk population is predicted to be 76.5%; this immunity may be genetic and, therefore, inherited. The modeling also predicts that 6.9% of White Females are born with a mutation necessary to cause breast cancer (the hereditary form) and, therefore, are at the highest risk of developing it. By contrast, 16.6% of White Females are born without any such mutation but are nonetheless susceptible to developing breast cancer (the sporadic form). The modeling determines the required number of ordered mutations for a cell to become cancerous as well as the mean time between consecutive mutations for both the sporadic and hereditary forms of the disease. The mean time between consecutive breast cancer mutations was found to vary between 2.59 - 2.97 years, suggesting that such mutations are rare events and establishing an upper bound on the lifetime of a breast cell. The prevalence of immunity to breast cancer is predicted to be 79.7% in Blacks, 86.5% in Asians, and 85.8% in Indians. Similarly, the prevalence of immunity to prostate cancer is predicted to be 67.4% for Whites, 50.5% for Blacks, 77.7% for Asians, and 78.6% for Indians. It is of paramount importance to delineate the mechanism underlying immunity to these cancers.
Mathematics Subject Classification: 92C60
Key words: cancer incidence / mutation model / immunity / sporadic / hereditary / pathways / proto-oncogene / immunosurveillance / cell lifetime
© EDP Sciences, 2010
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