A mathematical model of survival kinetics. I. Theoretical basis.

A mathematical model of mortality and survival kinetics is proposed based upon the two main aspects of survival data, namely, the rate of vitality reduction with age and its statistical distribution. Certain mathematical assumptions are made on the time-course of both vitality and its distribution. Then, these two aspects are integrated in a single model which can be used to describe survivorship, cumulative mortality or dying. The model is capable of fitting empirical curves even at very advanced ages, where the widely used Gompertz law fails. Examples are provided, derived from populations having rather different lifespans such as rotifers, flies, rats and horses. The model maintains one of the most interesting characteristics of Gompertz law, namely, the possibility to estimate the 'design constant for longevity' relating maximum lifespan to one of the parameters of the model. It also has the potential characteristics enabling it to be used to judge the statistical significance of the difference between two empirical survival curves.