A multivariate analysis on spatiotemporal evolution of Covid-19 in Brazil

Abstract

This data-driven work aims to analyze and classify the spatiotemporal distribution of all Brazilian states considering data so diverse as the number of Covid-19 cases, deaths, confirmed cases per 100 k inhabitants, mortality per 100 k inhabitants and case fatality rates as health indicators. We also considered population, area and population density as geographic indicators. Finally, GDP and HDI were taken into account as economic and social criteria. For this task data were collected from April 3rd until August 8th, 2020, corresponding to epidemiological weeks 14-32, reaching three million cases and a hundred thousand deaths. With this data it was possible to classify Brazilian states using multivariate methods into possible groups by means of non-hierarchical (k-means) cluster as well as factor analysis. It was possible to group all states plus the Federal District into five clusters, taking into account these 10 variables over the first five months of the epidemic. Group changes between states were observed over time and clusters, and between three and four factors were found. However, even with great difference on health indicators during days, the number of clusters remains fixed. Also, São Paulo and Rio de Janeiro states were ranked at top list taking into account all epidemiological weeks. Correlations were observed between variables, such as the number of Covid cases and deaths with GDP for most of epidemiological weeks. Some clusters were more critical due to specific variables, including cities that are main hotspots. These multivariate findings would provide a comprehensive description of the ongoing Covid-19 epidemic and may help to guide subsequent studies to understand and control virus transmission.

Keywords: COVID-19; Coronavirus; Factor analysis; K-means clustering; Pandemic; Spatiotemporal analysis.

Graphical abstract

Fig. 1

a-t). Elbow data charts with the optimal number of clusters in all cases, k^∗ = 5, obtained from the tangent method (the intercept between lines). Covid-19 cases were taken from April 3rd up to August 8th, 2020. The corresponding epidemiological weeks (EW) are indicated.

Fig. 2

a-t). Spatiotemporal evolution of Covid-19 in Brazilian states, that were grouped in five k-means clusters, from April 3rd up to August 8th, 2020. The corresponding epidemiological weeks (EW) are indicated, from 14 to 32.

Fig. 3

Loading plots with rotated loadings of EW 32 for components 1 and 2 (a) and components 2 and 3 (b). The first two components represent 57.032% of all variability, and components 2 and 3 represent 32.772% of all variability. From these figures is possible to group variables in three clusters, A, B, C: (confirmed cases or incidence per 100 k inhabitants, mortality per 100 k inhabitants), (case fatality rates, population density, area, HDI) and (number of Covid-19 cases, number of deaths, population, GDP), respectively.

Fig. 4

Spatiotemporal evolution of all five groups, from April 3rd up to August 8th, 2020. These dates correspond to epidemiological weeks (EW) 14–32. It is possible to note that three states changed groups twice (DF, PR, RS), eight ones changed three times (MG, MS, MT, PB, PE, RJ, SC, TO), fourteen changed four times (AC, AL, AM, AP, CE, ES, GO, MA, PA, PI, RN, RO, RR, SE) and just one state changed five times (BA). Only SP remained fixed.