Modeling the Evolution of Infectious Diseases with Functional Data Models: The Case of COVID-19 in Brazil

TL;DR

This paper uses functional data analysis to model and cluster COVID-19 death curves across regions in Brazil, and employs functional quantile regression to relate these curves to socioeconomic factors, improving prediction accuracy.

Contribution

It introduces a two-stage approach combining clustering of death curves and functional quantile regression with socioeconomic variables, enhancing understanding and prediction of COVID-19 evolution.

Findings

Identified heterogeneity in death curves across regions.

Functional quantile regression outperformed ordinary least squares in curve fitting.

Clusters served as alert levels for critical COVID-19 situations.

Abstract

In this paper, we apply statistical methods for functional data to explain the heterogeneity in the evolution of number of deaths of Covid-19 over different regions. We treat the cumulative daily number of deaths in a specific region as a curve (functional data) such that the data comprise of a set of curves over a cross-section of locations. We start by using clustering methods for functional data to identify potential heterogeneity in the curves and their functional derivatives. This first stage is an unconditional descriptive analysis, as we do not use any covariate to estimate the clusters. The estimated clusters are analyzed as "levels of alert" to identify cities in a possible critical situation. In the second and final stage, we propose a functional quantile regression model of the death curves on a number of scalar socioeconomic and demographic indicators in order to investigate their functional effects at different levels of the cumulative number of deaths over time. The proposed model showed a superior predictive capacity by providing better curve fit at different levels of the cumulative number of deaths compared to the functional regression model based on ordinary least squares.