  Confronting the pandemic of COVID-19, is nowadays one of the most prominent
challenges of the human species. A key factor in slowing down the virus
propagation is the rapid diagnosis and isolation of infected patients. The
standard method for COVID-19 identification, the Reverse transcription
polymerase chain reaction method, is time-consuming and in short supply due to
the pandemic. Thus, researchers have been looking for alternative screening
methods and deep learning applied to chest X-rays of patients has been showing
promising results. Despite their success, the computational cost of these
methods remains high, which imposes difficulties to their accessibility and
availability. Thus, the main goal of this work is to propose an accurate yet
efficient method in terms of memory and processing time for the problem of
COVID-19 screening in chest X-rays. Methods: To achieve the defined objective
we exploit and extend the EfficientNet family of deep artificial neural
networks which are known for their high accuracy and low footprints in other
applications. We also exploit the underlying taxonomy of the problem with a
hierarchical classifier. A dataset of 13,569 X-ray images divided into healthy,
non-COVID-19 pneumonia, and COVID-19 patients is used to train the proposed
approaches and other 5 competing architectures. Finally, 231 images of the
three classes were used to assess the quality of the methods. Results: The
results show that the proposed approach was able to produce a high-quality
model, with an overall accuracy of 93.9%, COVID-19, sensitivity of 96.8% and
positive prediction of 100%, while having from 5 to 30 times fewer parameters
than other than the other tested architectures. Larger and more heterogeneous
databases are still needed for validation before claiming that deep learning
can assist physicians in the task of detecting COVID-19 in X-ray images.
