Population dynamics model for aging

Jacques Demongeot; Pierre Magal; Jacques Demongeot; Pierre Magal

doi:10.3934/mbe.2023870

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 11: 19636-19660. doi: 10.3934/mbe.2023870

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Research article

Population dynamics model for aging

Jacques Demongeot ¹,
Pierre Magal ^{2
,
,}

1.
Université Grenoble Alpes, AGEIS EA7407, F-38700 La Tronche, France
2.
University of Bordeaux, IMB, UMR 5251, F-33400 Talence, France. CNRS, IMB, UMR 5251, F-33400 Talence, France

Received: 07 September 2023 Revised: 12 October 2023 Accepted: 15 October 2023 Published: 26 October 2023

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 negative (we then speak of rejuvenation) or positive (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.
- Nonlocal transport equations,
- Equation of moments of distributions,
- Rejuvenation and Premature aging,
- Biological age
Citation: Jacques Demongeot, Pierre Magal. Population dynamics model for aging[J]. Mathematical Biosciences and Engineering, 2023, 20(11): 19636-19660. doi: 10.3934/mbe.2023870

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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 negative (we then speak of rejuvenation) or positive (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.

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