Modification of a Numerical Method Using FIR Filters in a Time-dependent SIR Model for COVID-19

TL;DR

This paper introduces a modification to an existing FIR filter-based numerical method for a time-dependent SIR model to improve COVID-19 infection and recovery predictions, validated with real data from Minas Gerais, Brazil.

Contribution

The paper proposes a small modification to the FIR filter coefficient estimation algorithm, resulting in improved prediction accuracy for COVID-19 case modeling.

Findings

Modified algorithm yields better approximation errors.

Effective in tracking COVID-19 cases in Minas Gerais.

Demonstrates improved predictive performance over previous method.

Abstract

Authors Yi-Cheng Chen, Ping-En Lu, Cheng-Shang Chang, and Tzu-Hsuan Liu use the Finite Impulse Response (FIR) linear system filtering method to track and predict the number of people infected and recovered from COVID-19, in a pandemic context in which there was still no vaccine and the only way to avoid contagion was isolation. To estimate the coefficients of these FIR filters, Chen et al. used machine learning methods through a classical optimization problem with regularization (ridge regression). These estimated coefficients are called ridge coefficients. The epidemic mathematical model adopted by these researchers to formulate the FIR filters is the time-dependent discrete SIR. In this paper, we propose a small modification to the algorithm of Chen et al. to obtain the ridge coefficients. We then used this modified algorithm to track and predict the number of people infected and recovered from COVID-19 in the state of Minas Gerais/Brazil, within a prediction window, during the initial period of the pandemic. We also compare the predicted data with the respective real data to check how good the approximation is. In the modified algorithm, we set values for the FIR filter orders and for the regularization parameters, both different from the respective values defined by Chen et al. in their algorithm. In this context, the numerical results obtained by the modified algorithm in some simulations present better approximation errors compared to the respective approximation errors presented by the algorithm of Chen et al.