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This pandemic is viewed as a critical component of the fight against an enormous threat to the human population. Deep convolutional neural networks have recently proved their ability to perform well in classification and dimension reduction tasks. Selecting hyper-parameters is critical for these networks. This is because the search space expands exponentially in size as the number of layers increases. All existing approaches utilize a pre-trained or designed architecture as an input. None of them takes design and pruning into account throughout the process. In fact, there exists a convolutional topology for any architecture, and each block of a CNN corresponds to an optimization problem with a large search space. However, there are no guidelines for designing a specific architecture for a specific purpose; thus, such design is highly subjective and heavily reliant on data scientists\u2019 knowledge and expertise. Motivated by this observation, we propose a topology optimization method for designing a convolutional neural network capable of classifying radiography images and detecting probable chest anomalies and infections, including COVID-19. 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