Modelling perspectives on aging: can mathematics help us stay young?

Abstract

We survey several types of mathematical models that keep track of age distributions in a population, or follow some aspects of aging, such as loss of replicative potential of stem cells. The properties of a class of linear models of this type are discussed and compared. We illustrate the applicability of such models with a simple example based on hypothetical stem cell dynamics developed to address age-related telomere loss in the human granulocyte pool. We then describe the contrasting behaviour of nonlinear systems. Examples are drawn from the class of "dynamical diseases" to illustrate some of the aspects of nonlinear systems. Applications of these, and other models to the problems of aging and replicative aging are discussed.