In this work, Deep Bidirectional Recurrent Neural Networks (BRNNs) models were implemented based on both Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) cells in order to distinguish between genome sequence of SARS-CoV-2 and other Corona Virus strains such as SARS-CoV and MERS-CoV, Common Cold and other Acute Respiratory Infection (ARI) viruses. An investigation of the hyper-parameters including the optimizer type and the number of unit cells, was also performed to attain the best performance of the BRNN models. Results showed that the GRU BRNNs model was able to discriminate between SARS-CoV-2 and other classes of viruses with a higher overall classification accuracy of 96.8% as compared to that of the LSTM BRNNs model having a 95.8% overall classification accuracy. The best hyper-parameters producing the highest performance for both models was obtained when applying the SGD optimizer and an optimum number of unit cells of 80 in both models. This study proved that the proposed GRU BRNN model has a better classification ability for SARS-CoV-2 thus providing an efficient tool to help in containing the disease and achieving better clinical decisions with high precision.