Evolution of COVID-19 pandemic: Power-law growth and saturation

In this paper, we analyze the real-time infection data of COVID-19 epidemic for 21 nations up to June 30, 2020. For most of these nations, the total number of infected individuals exhibits a succession of exponential growth and power-law growth before the flattening of the curve. In particular, we find a universal <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20091389v3_inline1.gif"/></alternatives></inline-formula> growth before they reach saturation. However, at present, India, which has I(t) ~ t², and Russia and Brazil, which have I(t) ~ t, are yet to flatten their curves. Thus, the polynomials of the I(t) curves provide valuable information on the stage of the epidemic evolution, thus on the life cycle of COVID-19 pandemic. Besides these detailed analyses, we compare the predictions of an extended SEIR model and a delay differential equation-based model with the reported infection data and observed good agreement among them, including the <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20091389v3_inline2.gif"/></alternatives></inline-formula> behaviour. We argue that the power laws in the epidemic curves may be due to lockdowns.