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The objective of this study was to analyse the dynamics of spatial dispersion of the coronavirus disease 2019 (COVID-19) in Brazil by correlating them to socioeconomic indicators. This is an ecological study of COVID-19 cases and deaths between 26 February and 31 July 2020. All Brazilian counties were used as units of analysis. The incidence, mortality, Bayesian incidence and mortality rates, global and local Moran indices were calculated. A geographic weighted regression analysis was conducted to assess the relationship between incidence and mortality due to COVID-19 and socioeconomic indicators (independent variables). There were confirmed 2 662 485 cases of COVID-19 reported in Brazil from February to July 2020 with higher rates of incidence in the north and northeast. The Moran global index of incidence rate (0.50, P = 0.01) and mortality (0.45 with P = 0.01) indicate a positive spatial autocorrelation with high standards in the north, northeast and in the largest urban centres between cities in the southeast region. In the same period, there were 92 475 deaths from COVID-19, with higher mortality rates in the northern states of Brazil, mainly Amazonas, Pará and Amapá. The results show that there is a geospatial correlation of COVID-19 in large urban centres and regions with the lowest human development index in the country. In the geographic weighted regression, it was possible to identify that the percentage of people living in residences with density higher than 2 per dormitory, the municipality human development index (MHDI) and the social vulnerability index were the indicators that most contributed to explaining incidence, social development index and the municipality human development index contributed the most to the mortality model. We hope that the findings will contribute to reorienting public health responses to combat COVID-19 in Brazil, the new epicentre of the disease in South America, as well as in other countries that have similar epidemiological and health characteristics to those in Brazil.