On the dynamics of the Coronavirus epidemic and the unreported cases: the Chilean case

TL;DR

This paper models COVID-19 dynamics in Chile, emphasizing unreported cases and variable transmission rates, providing structural insights into the epidemic's progression and implications for future research.

Contribution

It applies a modified SIR model with variable transmission to Chile, incorporating unreported cases estimated via mortality rates, and analyzes its structural properties.

Findings

Convergence of susceptible population to a positive limit.

Non-uniqueness of epidemic peak maxima.

Effective modeling of unreported cases using mortality data.

Abstract

We analyze the dynamics of the COVID-19 epidemic taking into account the role of the unreported cases. After a first section in which we deal with a framework of very slow test capacity, we turn to the model recently introduced/implemented by Liu, Magal, Seydi and Webb. First, we prove some basic structural results for the corresponding ODE, as for instance the convergence of S(t) to a positive limit. These are similar to those of the classical SIR model, although the maxima of the corresponding curves are not necessarily unique. Finally, we implement the model -- but with a variable transmission rate -- in the Chilean context. A key parameter adjustment (namely, the fraction of unreported cases) is done via an argument using mortality rates. We conclude with several conclusions and lines of future research.