论文标题
统一传播疾病扩散范式与gompertzian的增长
Unifying the communicable disease spreading paradigm with Gompertzian growth
论文作者
论文摘要
许多研究表明，累积死亡率遵循了2020年3月至4月的初始大流行时期的Gompertz曲线。我们表明，Gompertz曲线与预期的初始逻辑生长曲线不相容，这是传统敏感受感染的感受感染的（SIR）模型的预期，并提出了一种在新的论文中，该模型可以更好地解释了具有无数的自然特征，从而可以更好地解释了具有验证性的自然特征。其次，我们表明，要使Gompertz曲线出现，干扰必须同时对每个人作用，拒绝疾病传播阶段的可能性。第三，我们通过使用高阶相互作用项来增强逻辑增长方程，并表明仅当传输网络中的所有节点与无限速度和相互作用通信时，我们将逻辑增长与Gompertzian的增长联系起来。至关重要的是，这种增强必须伴随着一种因果关系，其中增长来源不是感染者，而是易感人群的池。因此，我们发现了与现有的Richards模型（也称为$θ$ - 逻辑增长）之间的新颖桥梁和Gompertzian生长之间的新桥梁。
A number of studies have shown that cumulative mortality followed a Gompertz curve in the initial Covid pandemic period, March-April 2020. We show that the Gompertz curve is incompatible with expected initial logistic growth curves as predicted by traditional Susceptible-Infected-Recovered (SIR) models, and propose a new theory which better explains the nature of the mortality characteristics based on a global biosphere disturbance. Second, we show that for the Gompertz curve to emerge, the disturbance has to act on everyone simultaneously, rejecting the possibility of a disease propagation stage. Third, we connect logistic growth with Gompertzian growth by augmenting the logistic growth equation with higher order interaction terms, and show that the SIR model family is compatible with Gompertzian growth only when all nodes in the transmission network communicate with infinite speed and interaction. Crucially, this augmentation must be accompanied by a causality-reversal where the source of growth is not the pool of infected but the pool of susceptible people. We thus find a novel bridge between logistic and Gompertzian growth, separate from the existing Richards model (also called $θ$-logistic growth).
