COVID-19 is a positive-sense single-stranded RNA virus caused by a strain of coronavirus, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Several noteworthy variants of SARS-CoV-2 were declared by WHO as Alpha, Beta, Gamma, Delta, and Omicron. Till 13/Dec/2022, it has caused 6.65 million death tolls, and over 649 million confirmed positive cases. Based on the convolutional neural network (CNN), this study first proposes a ten-layer CNN as the backbone model. Then, the exponential linear unit (ELU) is introduced to replace ReLU, and the traditional convolutional block is now transformed into conv-ELU. Finally, an ELU-based CNN (ELUCNN) model is proposed for COVID-19 diagnosis. Besides, the MDA strategy is used to enhance the size of the training set. We develop a mobile app integrating ELUCNN, and this web app is run on a client–server modeled structure. Ten runs of the tenfold cross-validation experiment show our model yields a sensitivity of $$94.41\pm 0.98$$ 94.41 ± 0.98 , a specificity of $$94.84\pm 1.21$$ 94.84 ± 1.21 , an accuracy of $$94.62\pm 0.96$$ 94.62 ± 0.96 , and an F1 score of $$94.61\pm 0.95$$ 94.61 ± 0.95 . The ELUCNN model and mobile app are effective in COVID-19 diagnosis and give better results than 14 state-of-the-art COVID-19 diagnosis models concerning accuracy.