Department of Public Health Sciences, Stockholm University, Stockholm, Sweden.
PLoS One. 2020 Jun 4;15(6):e0233384. doi: 10.1371/journal.pone.0233384. eCollection 2020.
The risk of dying increases exponentially with age, in humans as well as in many other species. This increase is often attributed to the "accumulation of damage" known to occur in many biological structures and systems. The aim of this paper is to describe a generic model of damage accumulation and death in which mortality increases exponentially with age. The damage-accumulation process is modeled by a stochastic process know as a queue, and risk of dying is a function of the accumulated damage, i.e., length of the queue. The model has four parameters and the main characteristics of the model are: (i) damage occurs at random times with a constant high rate; (ii) the damage is repaired at a limited rate, and consequently damage can accumulate; (iii) the efficiency of the repair mechanism decays linearly with age; (iv) the risk of dying is a function of the accumulated damage. Using standard results from the mathematical theory of queues it is shown that there is an exponential dependence between risk of dying and age in these models, and that this dependency holds irrespective of how the damage-accumulation process is modeled. Furthermore, the ways in which this exponential dependence is shaped by the model parameters are also independent of the details of the damage accumulation process. These generic features suggest that the model could be useful when interpreting changes in the relation between age and mortality in real data. To exemplify, historical mortality data from Sweden are interpreted in the light of the model. The decrease in mortality seen between cohorts born in 1905, compared to those born in 1885, can be accounted for by higher threshold to damage. This fits well with the many advances made in public health during the 20th century.
随着年龄的增长,人类和许多其他物种的死亡风险呈指数级增加。这种增加通常归因于许多生物结构和系统中发生的“损伤积累”。本文的目的是描述一个损伤积累和死亡的通用模型,其中死亡率随年龄呈指数增长。损伤积累过程通过一个称为队列的随机过程来建模,死亡风险是累积损伤的函数,即队列的长度。该模型有四个参数,模型的主要特征是:(i)损伤随机发生,速率恒定较高;(ii)损伤以有限的速率修复,因此损伤可以积累;(iii)修复机制的效率随年龄线性下降;(iv)死亡风险是累积损伤的函数。使用队列数学理论的标准结果表明,在这些模型中,死亡风险与年龄之间存在指数关系,并且这种依赖性与损伤积累过程的建模方式无关。此外,模型参数如何塑造这种指数依赖性也与损伤积累过程的细节无关。这些通用特征表明,该模型在解释真实数据中年龄和死亡率之间的关系变化时可能有用。为了举例说明,根据该模型对瑞典的历史死亡率数据进行了解释。与 1885 年出生的人相比,1905 年出生的人之间的死亡率下降可以归因于损伤阈值的提高。这与 20 世纪公共卫生方面的许多进展非常吻合。