摘要翻译：
考虑了长寿生物体衰老过程的一个简单数学模型。这个模型的关键点是假设身体内部没有以几十年为单位计算时间的时钟。在这些尺度上，我们可以通过只考虑背景（平滑的、平均的）过程的经验来限制自己。人体是在处理内部的生物因素，这些因素可以被认为是生物钟在适当的参数化相应的变量。这些变量的动力学是用一个自治的ODES系统来描述的。考虑了方程组右手边的一种特殊表示形式，即二次多项式。在一个变量的最简单情况下，我们处理一个logistic方程，它有一个解析解。这种二次模型用于预测相对较小时间间隔内的老化过程动态是合理的。然而，由于可以对方程组的二次右边给出定义良好的生物学解释，我们可以预期这个简化经验模型的适用范围可以扩展到相对较大的时间间隔。我们认为，所考虑的模型是组织实验数据的一个良好而简单的数学框架。该模型可能有助于量化和安排因果关系链，这些因果关系链可能对衰老过程的发展具有重要意义。
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英文标题：
《Simple mathematical model of aging》
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作者：
Yu. N. Morokov
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最新提交年份：
2019
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分类信息：

一级分类：Quantitative Biology        数量生物学
二级分类：Other Quantitative Biology        其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
  A simple mathematical model of the aging process for long-lived organisms is considered. The key point in this model is the assumption that the body does not have internal clocks that count out the chronological time at scales of decades. At these scales, we may limit ourselves by empirical consideration only the background (smoothed, averaged) processes. The body is dealing with internal biological factors, which can be considered as the biological clocks in suitable parameterization of corresponding variables. The dynamics of these variables is described using a system of autonomous ODEs. A particular representation of the right-hand side of equations in the form of quadratic polynomials is considered. In the simplest case of one variable we deal with a logistic equation, which has an analytical solution. Such quadratic model is justified if it is used to predict the dynamic of aging process for relatively small time intervals. However, since a well-defined biological interpretation can be given for the quadratic right-hand side of the equations, we can expect that the area of applicability of this simplified empirical model can extend to relatively large time intervals. The considered model is, in our opinion, a good and simple mathematical framework for organizing experimental data. The model may be useful to quantify and arrange the chains of causal relationships that may appear significant for the development of the aging process.
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PDF链接：
https://arxiv.org/pdf/1912.08163