Philippe P
Department of Social and Preventive Medicine, Faculty of Medicine, University of Montreal, QC, Canada.
Hum Biol. 1993 Aug;65(4):525-46.
In this article I aim to provide some feeling of the new paradigm of disease causation (chaos) as it applies to the field of population biology and epidemiology. A secondary objective is to show, with the aid of qualitative methods, how one can approach chaos in time-series data. The multifactorial stochastic paradigm of causation is contrasted with the new deterministic approach. This approach is embedded in the theory of nonlinear system dynamics. Chaos implies that randomness is intrinsic to a nonlinear deterministic system; this is true despite the extent of knowledge of the intervening causes and, ultimately, despite determinism. Three research avenues are discussed in depth from the standpoint of chaos theory. First, the topic of sporadic epidemics is dealt with. I argue that the space-time clustering of cases from a starting epidemic is due to a sudden and high increase of the contact rate beyond a threshold. Interaction rather than main effects and nonlinear rather than linear dynamics are involved. Second, the incubation period of disease is studied. I advocate that an individual-level deterministic process underlies Sartwell's model of the incubation period. This accounts for the robustness of the model vis-à-vis confounding variables. Third, monozygotic twinning is analyzed. Assumed by some to be a random process, monozygotic twinning proves to be dynamically different from dizygotic or single-maternity processes; its dynamics can actually be chaotic. Throughout the provided examples, the point is made that chancelike phenomena are primarily concerned with chaos theory. For biological problems showing recurrent inconsistencies by stochastic modeling, dynamic modeling should be envisaged. Inconsistencies can suggest that the relevant factors are out of the model and that they are related deterministically. Finally, spectral analysis and attractors in the phase space are presented; these tools can aid the population biologist in tracing out chaos from time-series data sets. Several time-series data sets are simulated according to a simple nonlinear difference equation that bears some relationship to the basics of the dynamics of infections in the population. I show how the series can be analyzed and interpreted. Much research remains to be carried out until the nonlinear effects of risk factors can be validated. The undertaking is worth the effort, as a new paradigm of causation is at stake.
在本文中，我的目的是阐述疾病因果关系新范式（混沌）在群体生物学和流行病学领域中的应用情况。第二个目标是借助定性方法展示如何处理时间序列数据中的混沌现象。将多因素随机因果范式与新的确定性方法进行对比。这种方法根植于非线性系统动力学理论。混沌意味着随机性是一个非线性确定性系统所固有的；无论对中间原因的了解程度如何，最终无论是否具有确定性，都是如此。从混沌理论的角度深入讨论了三条研究途径。首先，探讨散发性流行病这一主题。我认为，起始流行病中病例的时空聚集是由于接触率突然大幅上升并超过某个阈值所致。涉及的是相互作用而非主要效应，是非线性动力学而非线性动力学。其次，研究疾病的潜伏期。我主张，个体层面的确定性过程是萨特韦尔潜伏期模型的基础。这解释了该模型相对于混杂变量的稳健性。第三，分析同卵双胞胎现象。一些人认为同卵双胞胎是一个随机过程，但事实证明它在动力学上与异卵双胞胎或单胎生育过程不同；其动力学实际上可能是混沌的。在所有给出的例子中，都表明类似机会的现象主要与混沌理论相关。对于通过随机建模显示出反复出现不一致性的生物学问题，应考虑动态建模。不一致性可能表明相关因素不在模型中，且它们具有确定性关联。最后，介绍了频谱分析和相空间中的吸引子；这些工具可帮助群体生物学家从时间序列数据集中找出混沌现象。根据一个与群体中感染动力学基础有一定关系的简单非线性差分方程模拟了几个时间序列数据集。我展示了如何对这些序列进行分析和解释。在能够验证风险因素的非线性效应之前，仍有许多研究有待开展。这项工作值得付出努力，因为一个新的因果关系范式正处于关键阶段。
