Physiological Aging as an Infinitesimally Ratcheted Random Walk

TL;DR

This paper introduces an infinitesimally ratcheted random walk model to accurately represent physiological aging, preventing backward movement in age distribution models like Langevin and Fokker-Planck equations.

Contribution

It proposes two novel mathematical formulations for modeling aging as a non-reversible process, improving upon traditional models that allow backward age movement.

Findings

The models prevent physiological age from decreasing over time.

Comparison shows the new models differ from Fokker-Planck in dynamics.

Analytical expressions for mean and variance are derived.

Abstract

The distribution of a population throughout the physiological age of the individuals is very relevant information in population studies. It has been modeled by the Langevin and the Fokker- Planck equations. A major problem with these equations is that they allow the physiological age to move back in time. This paper proposes an Infinitesimally ratcheted random walk as a way to solve that problem. Two mathematical representations are proposed. One of them uses a non-local scalar field. The other one is local, but involves a multi-component field of speed states. These two formulations are compared to each other and to the Fokker-Planck equation. The relevant properties are discussed. The dynamics of the mean and variance of the population age resulting from the two proposed formulations are obtained.