Quantifying the spread of communicable diseases with immigration of infectious individuals

TL;DR

This paper introduces new epidemiological thresholds to better understand and predict the spread of infectious diseases considering immigration of infected individuals, especially when traditional metrics like R0 are inadequate.

Contribution

It develops novel analytical indices for disease spread that account for infected immigration, with validation through a COVID-19 model using Chilean data.

Findings

New thresholds effectively predict disease dynamics.

Indices identify key parameters influencing disease spread.

Model shows good predictive accuracy with real data.

Abstract

We construct a set of new epidemiological thresholds to address the general problem of spreading and containment of a disease with influx of infected individuals when the classic $\mathcal R_0$ is no longer meaningful. We provide analytical properties of these indices and illustrate their usefulness in a compartmental model of COVID-19 with data taken from Chile showing a good predictive potential when contrasted with the recorded disease behaviour. This approach and the associated analytical and numerical results allow us to quantify the severity of an immigration of infectious individuals into a community, and identification of the key parameters that are capable of changing or reversing the spread of an infectious disease in specific models.