Mathematical Modeling and Georeferenced Forecasting for the COVID-19 at the State of RS, Brazil

Abstract

In this contribution, we present a predictive tool developed to help in the management of the evolution of the COVID-19 pandemic situation in Rio Grande do Sul (RS) - Brazil. This tool is the result of georeferenced data analysis, mathematical modeling, and parameter calibration for the dynamics of a SIR-type model defined on a spatial structure that allows distinct subpopulations to interact, similar to the controlled distancing (A_l for l = 1, ···, 21) groupings proposed by the RS government and public health authorities. The predictive analysis, updated biweekly, provides three distinct scenarios per month (milder, average, and severe) and is made available as WebSIGs (Geographic Information System - GIS). The forecast of the average scenario for each Al group is the result of a simulation of the proposed SIRtype dynamics with calibrated parameters derived from an augmented Lagrangian maximum a posteriori estimation and data on the number of infected cases made available by the RS Health Secretariat. The milder and severe scenarios are obtained from the average scenario, with changes in the contagion rates of each Al group. When compared to the number of infections reported in each Al group, the modeling predictions for a biweekly time window (the first two weeks) were quite satisfactory, with errors ranging from 0% to 5.13%, gradually increasing over time. Therefore, we suggest a biweekly re-calibration of the parameters and corresponding forecasts as a wise strategy.