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The Mathematical Mechanism of Biological Aging
North American Actuarial Journal ( IF 1.4 ) Pub Date : 2020-09-09 , DOI: 10.1080/10920277.2020.1775654
Boquan Cheng 1 , Bruce Jones 1 , Xiaoming Liu 1 , Jiandong Ren 1
Affiliation  

Despite aging being a universal and ever-present biological phenomenon, describing this aging mechanism in accurate mathematical terms—in particular, how to model the aging pattern and quantify the aging rate—has been an unsolved challenge for centuries. In this article, we propose a class of Coxian-type Markovian models that can provide a quantitative description of the well-known aging characteristics—the genetically determined, progressive, and essentially irreversible process. Our model has a unique structure, including a constant transition rate for the aging process, and a functional form for the relationship between aging and death with a shape parameter to capture the biologically deteriorating effect due to aging. The force of moving from one state to another in the Markovian process indicates the intrinsic biological aging force. The associated increasing exiting rate captures the external force of stress due to mortality risk on a living organism. The idea of the article is developed from Lin and Liu's paper, “Markov Aging Process and Phase-type Law of Mortality,” that was published in 2007. A big difference is that, in this article, our model uses a functional form for model parameters, which allows a parsimonious yet flexible representation for various aging patterns. Our proposed mathematical framework can be used to classify the aging pattern and the key parameters of the model can be used to measure and compare how human aging evolves over time and across populations.



中文翻译:

生物衰老的数学机制

尽管衰老是一种普遍存在的生物学现象,但用准确的数学术语描述这种衰老机制,尤其是如何建模衰老模式和量化衰老率,已是数百年来未解决的挑战。在本文中,我们提出了一类考克斯类型的马尔可夫模型,该模型可以对众所周知的衰老特征进行定量描述,这些衰老特征是遗传确定的,渐进的且本质上不可逆的过程。我们的模型具有独特的结构,包括用于衰老过程的恒定过渡速率,以及用于衰老和死亡之间关系的函数形式,其形状参数可捕获由于衰老而导致的生物恶化效应。在马尔可夫过程中从一种状态移动到另一种状态的力表明了内在的生物衰老力。相关的增加的退出率捕获了由于对活生物体的死亡风险而产生的压力的外力。本文的想法是根据Lin和Liu在2007年发表的论文《马尔可夫衰老过程和阶段性死亡率定律》发展而来的。最大的不同是,本文中的模型使用函数形式进行建模参数,可以简化和灵活地表示各种老化模式。我们提出的数学框架可用于对衰老模式进行分类,模型的关键参数可用于度量和比较人类衰老如何随时间和跨人群发展。2007年出版的《马尔可夫衰老过程和阶段性死亡率定律》。最大的不同是,在本文中,我们的模型使用函数形式表示模型参数,从而可以简化而灵活地表示各种衰老模式。我们提出的数学框架可用于对衰老模式进行分类,模型的关键参数可用于度量和比较人类衰老如何随时间和跨人群发展。2007年出版的“马尔可夫衰老过程和死亡率的阶段型定律”。最大的不同是,在本文中,我们的模型使用函数形式表示模型参数,从而可以简化而灵活地表示各种衰老模式。我们提出的数学框架可用于对衰老模式进行分类,模型的关键参数可用于度量和比较人类衰老如何随时间和跨人群发展。

更新日期:2020-09-09
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