`Computational and Mathematical Methods in MedicineVolume 11 (2010), Issue 2, Pages 119-159doi:10.1080/17486700902910076`
Original Article

## Calculating the Number of People with Alzheimer's Disease in any Country Using Saturated Mutation Models of Brain Cell Loss that also Predict Widespread Natural Immunity to the Disease

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

Received 3 May 2007; Accepted 16 March 2009

Copyright © 2010 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 mutations that cause brain cells to spontaneously and randomly die leading to Alzheimer's disease (AD) is modelled. The prevalence of AD as a function of age in males and females is calculated from two very different mutation models of brain cell death. Once the prevalence functions are determined, the number of people with AD in any country or city can be estimated.

The models developed here depend on three independent parameters: the number of mutations necessary for a brain cell associated with AD to spontaneously die, the average time between mutations, and the fraction of the risk population that is immune to developing the disease, if any. The values of these parameters are determined by fitting the model's AD incidence function to the incidence data.

The best fits to the incidence rate data predict that as much as 74.1% of males and 79.5% of females may be naturally immune to developing AD. Thus, the development of AD is not a normal or inevitable result of the aging process. These fits also predict that males and females develop AD through different pathways, requiring a different number of mutations to cause the disease. The number of people in the USA with AD in the year 2000 is estimated to be 451,000.

It is of paramount importance to determine the nature of the immunity to AD predicted here. Finding ways of blocking the mutations leading to the random, spontaneous death of memory brain cells would prevent AD from developing altogether.