论文标题
随着年龄的年龄而导致的死亡率呈指数增长是一个简单的损害积累和死亡模型系统的通用特性
Exponential increase in mortality with age is a generic property of a simple model system of damage accumulation and death
论文作者
论文摘要
死亡的风险随着年龄，人类以及许多其他物种而呈指数增长。这种增加通常归因于许多生物结构和系统中已知发生的“损害的积累”。本文的目的是描述损害积累和死亡的通用模型，其中死亡率随着年龄的增长而成倍增加。损害蓄能过程以随机过程称为队列进行建模，而死亡的风险是累积损害的函数，即队列的长度。该模型具有四个参数，该模型的主要特征是：（i）损坏在随机时间内以恒定的高速率发生； （ii）损坏以有限的速度修复，因此损坏会累积； （iii）维修机制的效率随着年龄的增长而线性衰减； （iv）死亡的风险是累积损害的函数。使用排队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依赖性，并且这种依赖性无疑是如何建模损害造成的过程。此外，该指数依赖性由模型参数塑造的方式也独立于损害累积过程的细节。这些通用特征表明，在解释实际数据中年龄和死亡率之间的关系变化时，该模型可能很有用。为了进行检查，根据模型来解释瑞典的历史死亡率数据。与1885年出生的人群相比，出生于1905年的人群之间的死亡率下降可以通过更高的损害阈值来解释。这非常适合20世纪公共卫生的许多进步。
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 examplify, 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.
