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

J. C. Marques, A. De Cezaro, D. C. L. Alves, P. V. A. B. Lisbôa, M. Lazo, D. A. Sales


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.


COVID-19 forecast; SIR-type model, parameter calibration, georeferenced data.

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W. H. Organization, “Who coronavirus disease (covid-19) dashboard,” 2020/7/29, 2020.

V. R. . Z. J. Albani, V.V.L., “Estimating, monitoring, and forecasting covid-19 epidemics: a spatiotemporal approach applied to nyc data.,” Sci Rep, vol. 11, p. 9089, 2021.

J. Govaert, “Coronavirus: UK changes course amid death toll fears.,” https:// www. bbc. com/ news/ health-51915302 , 2020.

M. J. Lazo and A. De Cezaro, “Why can we observe a plateau even in an out of control epidemic outbreak? A SEIR model with the interaction of n distinct populations for Covid-19 in Brazil,” 2020.

D. P. de Paula, D. H. Miranda de Medeiros, E. Lacerda Barros, R. G. Pinheiro Guerra, J. d. O. Santos, J. S. Queiroz Lima, and R. M. Leite Monteiro, “Diffusion of covid-19 in the northern metropolis in northeast brazil: territorial dynamics and risks associated with social vulnerability,” Sociedade & Natureza, vol. 32, pp. 639–656, set. 2020.

M. d. G. Albuquerque, J. R. d. Santos, A. F. Silveira, D. L. Bornia Junior,

R. B. Nunes, T. B. R. Gandra, A. L. C. d. Silva, G. B. d. Miranda, and A. R.

Trevisol, “Influence of socio-economic indicators and territorial networks at the spatiotemporal spread dynamics of covid-19 in brazil,” Sociedade & Natureza, vol. 33, abr. 2021.

R. Ferreira, “Atlas, cibercartografia e neogeografia,” Revista Portuguesa de Estudos Regionais, pp. 31–44, 02 2016.

A. De Cezaro and et. all., “Georeferenced data from the COVID-19 pandemic for the state of Rio Grande do Sul: Reported positive cases and simulated forecasts,” Latin American Data in Science, vol. 1, p. 49–62, Nov. 2021.

P. Longley, “Geographical information systems: a renaissance of geodemographics for public service delivery,” Progress in Human Geography, vol. 29, no. 1, pp. 57–63, 2005.

W. Kermack and A. Mckendrick, “A contribution to the mathematical theory of epidemics,” Proceedings of the Royal Society of London. Series A, Containing papers of a Mathematical and Physical Character, vol. 115, no. 772, pp. 700–721, 1927.

H. W. Hethcote, “The mathematics of infectious diseases,” SIAM review, vol. 42, no. 4, pp. 599–653, 2000.

L. Rodrigues, M. Varriale, W. Godoy, and D. Mistro, Coupled Map Lattice Model for Insects and Spreadable Substances, pp. 141–169. 09 2014.

L. Perko, Differential Equations and Dynamical Systems. Springer, 2001.

A. De Cezaro, A. Marinho de Oliveira, and F. Travessini De Cezaro, Identificação de parâmetros em Equações Diferenciais: Teoria e Aplicações. UFPI, 2012.

G. Chowell, “Fitting dynamic models to epidemic outbreaks with quantified uncertainty: a primer for parameter uncertainty, identifiability, and forecasts,” Infectious Disease Modelling, vol. 2, no. 3, pp. 379–398, 2017.

A. De Cezaro, On a Parabolic Inverse Problem Arising in Quantitative Finance: Convex and Iterative Regularization. PhD Theses- IMPA, 2010.

A. De Cezaro, O. Scherzer, and J. Zubelli, “Convex regularization of local volatility models from option prices: Convergence analysis and rates,” Non-linear Analysis: Theory, Methods Applications, vol. 75, no. 4, pp. 2398–2415, 2012.

D. Bertsekas, Constrained optimization and Lagrange multiplier methods. Computer Science and Applied Mathematics, New York: Academic Press, 1982.

R. Rockafellar and R.-B. Wets, Variational analysis, vol. 317 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Berlin: Springer-Verlag, 1998.


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