As the ongoing COVID-19 pandemic passes from an acute to a chronic situation, countries and territories are grappling with the issue of how to reopen safely. The unique kinetics of infectivity of SARS-CoV-2, with its significant presymptomatic transmission, presents an unprecedented challenge to our intuitions. In this context, a generalizable quantitative understanding of the impact of SARS-CoV-2 infectivity on disease control strategies is vital. We used a previously published time-dependent model of SARS-CoV-2 infectivity (He et al., 2020) to parameterize an epidemiological model of transmission, which was then used to explore the effect of various disease control measures. Our analysis suggests that using symptom-based isolation alone as a control strategy is ineffective in limiting the spread of COVID-19, in contrast to its effectiveness in other diseases, such as SARS and influenza. Additionally, timeliness of testing and tracing strategies to reduce time to isolation, along with widespread adoption of measures to limit transmission are critical for any containment strategy. Our findings suggest that for symptom-based isolation and testing strategies to be effective, reduced transmission is required, reinforcing the importance of measures to limit transmission. From a public health strategy perspective, our findings lend support to the idea that symptomatic isolation should not form the primary basis for COVID-19 disease control.