Simple mathematical model of aging

TL;DR

This paper introduces a simple quadratic ODE-based mathematical model to describe the aging process in long-lived organisms, emphasizing biological factors over internal clocks and aiming to organize experimental data.

Contribution

It proposes a novel, simple quadratic ODE model for aging that can be applied over large time intervals and helps organize experimental aging data.

Findings

The model uses quadratic polynomials in autonomous ODEs.

Analytical solutions are available for the one-variable case.

The model is applicable for predicting aging dynamics over extended periods.

Abstract

A simple mathematical model of the aging process for long-lived organisms is considered. The key point in this model is the assumption that the body does not have internal clocks that count out the chronological time at scales of decades. At these scales, we may limit ourselves by empirical consideration only the background (smoothed, averaged) processes. The body is dealing with internal biological factors, which can be considered as the biological clocks in suitable parameterization of corresponding variables. The dynamics of these variables is described using a system of autonomous ODEs. A particular representation of the right-hand side of equations in the form of quadratic polynomials is considered. In the simplest case of one variable we deal with a logistic equation, which has an analytical solution. Such quadratic model is justified if it is used to predict the dynamic of aging process for relatively small time intervals. However, since a well-defined biological interpretation can be given for the quadratic right-hand side of the equations, we can expect that the area of applicability of this simplified empirical model can extend to relatively large time intervals. The considered model is, in our opinion, a good and simple mathematical framework for organizing experimental data. The model may be useful to quantify and arrange the chains of causal relationships that may appear significant for the development of the aging process.