Quadratic growth during the COVID-19 pandemic: merging hotspots and reinfections

TL;DR

This paper analyzes the quadratic growth pattern of COVID-19 cases, explaining it through spatial merging of infection sites and reinfections, supported by a spatial epidemiological model.

Contribution

It introduces a spatial epidemiological model that accounts for merging hotspots and reinfections to explain COVID-19 growth dynamics.

Findings

Quadratic growth persisted for about forty days during early COVID-19 spread.

Merging of disconnected sites explains the transition from exponential to quadratic growth.

Reinfections and their rate changes influence subsequent growth variations.

Abstract

The existence of an exponential growth phase during early stages of a pandemic is often taken for granted. However, for the 2019 novel coronavirus epidemic, the early exponential phase lasted only for about six days, while the quadratic growth prevailed for forty days until it spread to other countries and continued, again quadratically, but with a larger coefficient. Here we show that this rapid phase is followed by a subsequent slow-down where the coefficient is reduced to almost the original value at the outbreak. This can be explained by the merging of previously disconnected sites that occurred after the disease jumped (nonlocally) to a relatively small number of separated sites. Subsequent variations in the slope with continued growth can qualitatively be explained as a result of reinfections and changes in their rate. We demonstrate that the observed behavior can be described by a standard epidemiological model with spatial extent and reinfections included. Time-dependent changes in the spatial diffusion coefficient can also model corresponding variations in the slope.