Unifying the communicable disease spreading paradigm with Gompertzian growth

TL;DR

This paper challenges traditional epidemic models by showing that Gompertzian growth better explains initial COVID-19 mortality patterns and introduces a new theory linking biosphere disturbance to disease spread.

Contribution

It proposes a novel theory connecting global biosphere disturbance with Gompertzian growth and extends logistic models with higher order interactions to unify growth paradigms.

Findings

Gompertz curve incompatible with traditional SIR models.

Disturbance must act simultaneously on all individuals for Gompertzian growth.

Augmented logistic model links Gompertzian and logistic growth with higher order interactions.

Abstract

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 $\theta$-logistic growth).