The infectious disease Covid-19 has been causing severe social, economic, and human suffering across the globe since 2019. The countries have utilized different strategies in the last few years to combat Covid-19 based on their capabilities, technological infrastructure, and investments. A massive epidemic like this cannot be controlled without an intelligent and automatic health care system. The first reaction to the disease outbreak was lockdown, and researchers focused more on developing methods to diagnose the disease and recognize its behavior. However, as the new lifestyle becomes more normalized, research has shifted to utilizing computer-aided methods to monitor, track, detect, and treat individuals and provide services to citizens. Thus, the Internet of things, based on fog-cloud computing, using artificial intelligence approaches such as machine learning, and deep learning are practical concepts. This article aims to survey computer-based approaches to combat Covid-19 based on prevention, detection, and service provision. Technically and statistically, this article analyzes current methods, categorizes them, presents a technical taxonomy, and explores future and open issues.