Endemic infectious states below the epidemic threshold and beyond herd immunity

TL;DR

This paper introduces a modified SIR model with external infection inflow to explain persistent low-level epidemic states observed in COVID-19, challenging traditional epidemic threshold concepts.

Contribution

It presents a simple yet effective modification of the SIR model that captures long-living epidemic states and provides analytical insights into their dynamics.

Findings

Model reproduces COVID-19 data features in England.

Identifies epidemic states below and above the traditional threshold.

Challenges existing understanding of epidemic thresholds.

Abstract

In the recent COVID-19 pandemic we assisted at a sequence of epidemic waves intertwined by anomalous fade-outs with periods of low but persistent epidemic prevalence. These long-living epidemic states complicate epidemic control and challenge current modeling approaches as classical epidemic models fail to explain their emergence. Inspired by this phenomenon, we propose a simple mechanism able to reproduce several features observed in real data. Specifically, here we introduce a modification of the Susceptible-Infected-Recovered (SIR) model in a meta-population framework where a small inflow of infected individuals accounts for undetected internal or imported cases. Focusing on a regime where this external seeding is so small that cannot be detected from the analysis of epidemic curves, we find that outbreaks of finite duration percolate in time resulting in overall low but long-living epidemic states below and above the epidemic threshold. Using a two-state description of the local dynamics, we can extract analytical predictions for the phase space. The comparison with epidemic data demonstrates that our model is able to reproduce some critical signatures observed in COVID-19 spreading in England. Finally, our findings defy our understanding of the concept of epidemic threshold and its relationship with outbreaks survival for disease control.