Models of evolution based on data for spatio-temporal analysis of COVID-19 in Brazilian states
Résumé
In March 2020, the World Health Organization (WHO) defined the outbreak of COVID-19 disease, caused by the SARS-CoV-2 virus, like a pandemic. In the meantime, the first cases of COVID-19 in Brazil were identified. Despite the start of the vaccination campaign in Brazil in January 2021 and in several other countries, the demand for immunizers is still much higher than the supply of doses. Thus, the pandemic should still be a reality for a long time, requiring actions of surveillance, mitigation, or even suppression of the cycle of transmission of the disease. Mathematical-computational models are important tools for the analysis and diagnosis of the pandemic, which can indicate how to prevent new outbreaks or how to control current ones. Such models can also help to understand qualitative and quantitative characteristics of the propagation process of COVID-19, establishing cause and effect relationships that are vital to guide decision making. Epidemiological data record the history of the pandemic's evolution since its beginnings, encapsulating, among many characteristics, the effects of accelerating or reducing the spread of contagion due to the change in the social behavior of the population of interest. Although these data are subject to the effects of underreporting and delay, there is already a significant amount of spatio-temporal information accumulated in them (12 months of evolution, in all Brazilian cities). Thus, such data emerge as an important source of information about the dynamics of COVID-19, which can be explored (without ad hoc considerations) via machine / artificial intelligence learning techniques, with a view to extracting coherent structures/patterns that reveal relevant characteristics about the spread of the disease in Brazilian soil. This work proposes to develop a study of the spatial-temporal dynamics of COVID-19 in Brazilian states, using models based purely on data, ie, without any ad hoc hypothesis, constructed with the aid of two state-of-the-art techniques in statistical learning, they are: (i) Dynamic Mode Decomposition (DMD), which in some sense combines dimension reduction (principal component analysis) and spectral content analysis (Fourier transform) to extract coherent patterns in spatiotemporal data; (ii) Sparse Identification of Nonlinear Dynamics (SINDy), which seeks to reconstruct in a non-parametric way the law of evolution associated with data, imposing a sparse representation (which facilitates interpretation) to the function dictionary that generates the identified equations. COVID-19 data from Brazilian states and capitals are used to test the proposed framework.