Population dynamics model for aging

TL;DR

This paper introduces a mathematical model for biological age that accounts for both continuous aging and discontinuous jumps, capturing complex aging processes influenced by endogenous and exogenous factors.

Contribution

It proposes a novel mathematical framework for biological age dynamics, including jump processes, with proven existence, uniqueness, and analysis of the model's behavior.

Findings

Model captures positive and negative jumps in biological age.

Existence and uniqueness of the model solution are established.

Simulations illustrate the model's dynamic behavior.

Abstract

The chronological age used in demography describes the linear evolution of the life of a living being. The chronological age cannot give precise information about the exact developmental stage or aging processes an organism has reached. On the contrary, the biological age (or epigenetic age) represents the true evolution of the tissues and organs of the living being. Biological age is not always linear and sometimes proceeds by discontinuous jumps. These jumps can be positive (we then speak of rejuvenation) or negative (in the event of premature aging), and they can be dependent on endogenous events such as pregnancy (negative jump) or stroke (positive jump) or exogenous ones such as surgical treatment (negative jump) or infectious disease (positive jump). The article proposes a mathematical model of the biological age by defining a valid model for the two types of jumps (positive and negative). The existence and uniqueness of the solution are solved, and its temporal dynamic is analyzed using a moments equation. We also provide some individual-based stochastic simulations.