  Purpose: This paper proposes a methodology and a computational tool to study
the COVID-19 pandemic throughout the world and to perform a trend analysis to
assess its local dynamics.
  Methods: Mathematical functions are employed to describe the number of cases
and demises in each region and to predict their final numbers, as well as the
dates of maximum daily occurrences and the local stabilization date. The model
parameters are calibrated using a computational methodology for numerical
optimization. Trend analyses are run, allowing to assess the effects of public
policies. Easy to interpret metrics over the quality of the fitted curves are
provided. Country-wise data from the European Centre for Disease Prevention and
Control (ECDC) concerning the daily number of cases and demises around the
world are used, as well as detailed data from Johns Hopkins University and from
the Brasil.io project describing individually the occurrences in United States
counties and in Brazilian states and cities, respectively. U. S. and Brazil
were chosen for a more detailed analysis because they are the current foci of
the pandemic.
  Results: Illustrative results for different countries, U. S. counties and
Brazilian states and cities are presented and discussed.
  Conclusion: The main contributions of this work lie in (i) a straightforward
model of the curves to represent the data, which allows automation of the
process without requiring interventions from experts; (ii) an innovative
approach for trend analysis, whose results provide important information to
support authorities in their decision-making process; and (iii) the developed
computational tool, which is freely available and allows the user to quickly
update the COVID-19 analyses and forecasts for any country, United States
county or Brazilian state or city present in the periodic reports from the
authorities.
