The sudden spread of COVID-19 infections in a region can catch its healthcare system by surprise. Can one anticipate such a spread and allow healthcare administrators to prepare for a surge a priori? We posit that the answer lies in distinguishing between two types of waves in epidemic dynamics. The first kind resembles a spatio-temporal diffusion pattern. Its gradual spread allows administrators to marshal resources to combat the epidemic. The second kind is caused by super-spreader events, which provide shocks to the disease propagation dynamics. Such shocks simultaneously affect a large geographical region and leave little time for the healthcare system to respond. We use time-series analysis and epidemiological model estimation to detect and react to such simultaneous waves using COVID-19 data from the time when the B.1.617.2 (Delta) variant of the SARS-CoV-2 virus dominated the spread. We first analyze India’s second wave from April to May 2021 that overwhelmed the Indian healthcare system. Then, we analyze data of COVID-19 infections in the United States (US) and countries with a high and low Indian diaspora. We identify the Kumbh Mela festival as the likely super-spreader event, the exogenous shock, behind India’s second wave. We show that a multi-area compartmental epidemiological model does not fit such shock-induced disease dynamics well, in contrast to its performance with diffusion-type spread. The insufficient fit to infection data can be detected in the early stages of a shock-wave propagation and can be used as an early warning sign, providing valuable time for a planned healthcare response. Our analysis of COVID-19 infections in the US reveals that simultaneous waves due to super-spreader events in one country (India) can lead to simultaneous waves in other places. The US wave in the summer of 2021 does not fit a diffusion pattern either. We postulate that international travels from India may have caused this wave. To support that hypothesis, we demonstrate that countries with a high Indian diaspora exhibit infection growth soon after India’s second wave, compared to countries with a low Indian diaspora. Based on our data analysis, we provide concrete policy recommendations at various stages of a simultaneous wave, including how to avoid it, how to detect it quickly after a potential super-spreader event occurs, and how to proactively contain its spread.