A Mathematical Model of Aging Processes

Abstract

The present study attempts to develop a mathematical model which relates the amount of deterioration at a given age to the corresponding probability of death from a related cause for an individual at that age. That is, it is hoped to obtain a reliable index to determine an individual's level of health and to relate this level to a probability of death. The proposed model is an extension of a model mentioned by simms (1942). The simple model presented defines two mathematical parameters, R and S, which depend on the physiological process under consideration, and a cut-off level which relates the amount of deterioration to the chance of dying. Ontario mortality data are examined in light of the model and estimates of the values of R and S are obtained from the data by means of maximum likelihood methods. The fit, using the x2 statistic, between theoretical and observed mortality rates, is shown to be good for mortality rates from a number of causes-of-death and from all causes.

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