The emergence of the 2019 novel coronavirus (COVID-19) which was declared a pandemic has spread to 210 countries worldwide. It has had a significant impact on health systems and economic, educational and social facets of contemporary society. As the rate of transmission increases, various collaborative approaches among stakeholders to develop innovative means of screening, detecting and diagnosing COVID-19’s cases among human beings at a commensurate rate have evolved. Further, the utility of computing models associated with the fourth industrial revolution technologies in achieving the desired feat has been highlighted. However, there is a gap in terms of the accuracy of detection and prediction of COVID-19 cases and tracing contacts of infected persons. This paper presents a review of computing models that can be adopted to enhance the performance of detecting and predicting the COVID-19 pandemic cases. We focus on big data, artificial intelligence (AI) and nature-inspired computing (NIC) models that can be adopted in the current pandemic. The review suggested that artificial intelligence models have been used for the case detection of COVID-19. Similarly, big data platforms have also been applied for tracing contacts. However, the nature-inspired computing (NIC) models that have demonstrated good performance in feature selection of medical issues are yet to be explored for case detection and tracing of contacts in the current COVID-19 pandemic. This study holds salient implications for practitioners and researchers alike as it elucidates the potentials of NIC in the accurate detection of pandemic cases and optimized contact tracing.