In this brief work we present a novel approach to the logistic dynamics of populations and epidemic spreading that can take into account of the complex nature of such a process in several real situations, where due to different agents the dynamics is no longer characterized by a single characteristic timescale, but conversely by a distribution of time scales, rendered via a time-dependent growth rate. In detail, a differential equation containing a power-law time dependent growth rate is proposed, whose solution, named Stretched Logistic Function, provides a modified version of the usual logistic function. The model equation is inspired by and applied to the recent spreading on COVID-19 disease in Italy, showing how the real dynamics of infection spreading is characterized by a time dependent dynamics. A speculative discussion of the Stretched Logistic Function in relation to diffusion processes is attempted.

在这篇简短的工作中，我们提出了一种研究人口和流行病传播的逻辑动态的新方法，该方法可以考虑到在几种实际情况下这一过程的复杂性，其中由于不同的代理，动态不再以单一的特征为特征。特征时间尺度，但相反，通过时间尺度的分布，通过时间相关的增长率呈现。具体来说，提出了一个包含幂律时间依赖性增长率的微分方程，其解称为“拉伸逻辑函数” ，提供了通常逻辑函数的修改版本。该模型方程的灵感来自于最近在意大利传播的 COVID-19 疾病，并应用于该疾病，显示了感染传播的真实动态如何以时间依赖性动态为特征。尝试对与扩散过程相关的拉伸逻辑函数进行推测性讨论。