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

Abstract

AbstractCoronavirus 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 economy1–3. Exponential growth of infections was thought to be the defining feature of an epidemic in its initial growth phase4–7; any variation from an exponential growth was described by adjusting the parameters of the exponential model7,8. 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.