COVID-19 Pandemic: Power Law Spread and Flattening of the Curve

Abstract

In this paper, we analyze the real-time infection data of COVID-19 epidemic for nine nations. Our analysis is up to May 04, 2020. South Korea, China, Italy, France, Spain, and Germany have either flattened or close to flattening their epidemic curves. USA and Japan have transitioned to a linear regime, while India is still in a power-law phase. We argue that the transition from an exponential regime to a succession of power-law regimes is a good indicator for flattening of the epidemic curve. We also argue that lockdowns, long-term community transmission, and the transmission by asymptomatic carriers traveling long distances may be inducing the power-law growth of the epidemic.

Keywords: COVID-19; Epidemic spread; Power law growth.

Fig. 1

(color online) For the COVID-19 epidemic, the semi-logy plots of total infected individuals (I(t)) vs. time (t) (red thin curves) for the nine nations. We also plot $\dot{I}(t)$ vs. t (blue thick curves). The black dotted curves represent the best-fit curves. For the best-fit functions, refer to Table 1

Fig. 2

(color online) For COVID-19 epidemic: Schematic plots for I(t) and its derivative $\dot{I}(t)$ vs. t. S1, S2, S3, S4 represent the four stages of the epidemic: exponential growth in count ($exp(\beta t)$), power law growth ($t^n$), linear growth (t), and flat