Courant Institute of Mathematical Sciences, New York, USA.
Bull Math Biol. 2019 Apr;81(4):1070-1088. doi: 10.1007/s11538-018-00558-w. Epub 2018 Dec 17.
We suggest an explanation of typical incubation times statistical features based on the universal behavior of exit times for diffusion models. We give a mathematically rigorous proof of the characteristic right skewness of the incubation time distribution for very general one-dimensional diffusion models. Imposing natural simple conditions on the drift coefficient, we also study these diffusion models under the assumption of noise smallness and show that the limiting exit time distributions in the limit of vanishing noise are Gaussian and Gumbel. Thus, they match the existing data as well as the other existing models do. The character of our models, however, allows us to argue that the features of the exit time distributions that we describe are universal and manifest themselves in various other situations where the times involved can be described as detection or halting times, for example response times studied in psychology.
我们基于扩散模型的退出时间的普遍行为，对典型潜伏期的统计特征提出一种解释。我们给出了一维扩散模型中潜伏期分布具有典型右偏特征的严格数学证明。对扩散系数施加自然简单的条件，我们还研究了这些扩散模型在噪声较小的假设下的情况，并表明在噪声趋于零时的极限退出时间分布是高斯分布和 Gumbel 分布。因此，它们与现有数据以及其他现有模型吻合。然而，我们模型的特点使我们能够认为，我们所描述的退出时间分布特征是普遍的，并在其他各种情况下表现出来，例如在心理学中研究的反应时间等，可以将所涉及的时间描述为检测或停止时间。
