Since the beginning of the coronavirus (COVID-19) global pandemic, digital contact-tracing applications (apps) have been at the centre of attention as a digital tool to enable citizens to monitor their social distancing, which appears to be one of the leading practices for mitigating the spread of airborne infectious diseases. Many countries have been working towards developing suitable digital contact-tracing apps to allow the measurement of the physical distance between citizens and to alert them when contact with an infected individual has occurred. However, the adoption of digital contact-tracing apps has faced several challenges so far, including interoperability between mobile devices and users’ privacy concerns. There is a need to reach a trade-off between the achievable technical performance of new technology, false-positive rates, and social and behavioural factors. This paper reviews a wide range of factors and classifies them into three categories of technical, epidemiological and social ones, and incorporates these into a compact mathematical model. The paper evaluates the effectiveness of digital contact-tracing apps based on received signal strength measurements. The results highlight the limitations, potential and challenges of the adoption of digital contact-tracing apps.