Extreme COVID-19 waves reveal hyperexponential growth and finite-time singularity

Coronavirus disease 2019 (COVID-19) has rapidly spread throughout our planet, bringing human lives to a standstill. Understanding the early transmission dynamics helps plan intervention strategies such as lockdowns that mitigate further spread, minimizing the adverse impact on humanity and the economy ^1–3 . Exponential growth of infections was thought to be the defining feature of an epidemic in its initial growth phase ^4–7 ; any variation from an exponential growth was described by adjusting the parameters of the exponential model ^7,8 . Here, we show that, contrary to common belief, early stages of extreme COVID-19 waves display an unbounded growth and finite-time singularity accompanying a hyperexponential power-law. The faster than exponential growth phase is hazardous and would entail stricter regulations. Such a power-law description allows us to characterize COVID-19 waves with single power-law exponents, better than piece-wise exponentials. Furthermore, we identify the presence of log-periodic patterns decorating the power-law growth. These log-periodic oscillations may enable better prediction of the finite-time singularity. We anticipate that our findings of hyperexponential growth and log-periodicity will help model the COVID-19 transmission more accurately.