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

Abstract

In this paper, we analyze the real-time infection data of COVID-19 epidemic for 21 nations up to May 18, 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 √ t growth before they reach saturation. India, Singapore, and Sri Lanka have reached up to linear growth (I(t) ∼ t), and they are yet to flatten their curves. Russia and Brazil are still in the power-law (t 2 ) growth regime. Thus, the polynomials of the I(t) curves provide valuable information on the stage of the epidemic evolution. 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 √ t behaviour.

Evolution of COVID-19 Pandemic in India

“…The time series for both I(t) and D(t) follow exponential regimes during the early phases of the pandemic and subsequently transition to power-law regimes. This is in accordance with the earlier work of Verma et al [36] and Chatterjee et al [8]. The bestfit functions along with their relative errors are listed in Tables 1 and 2 for the infected and death cases respectively.…”

“…This may be attributed to immunity developed in the population [33,16] and better treatment of critical cases (plasma therapy, more ventilators, early detection, etc.). At the initial stage, the death rate and infection rate are nearly proportional to each other, consistent with the earlier observation of Chatterjee et al [8]. We also observe that at present, the infection count in .…”

“…Verma et al [36] and Chatterjee et al [8] analyzed infection counts of 21 leading countries. They observed the emergence of power-laws after an initial exponential phase.…”

Power law behaviour in the saturation regime of fatality curves of the COVID-19 pandemic

“…Power-law behaviour is a distinct signature of complexity, and in such a guise they are expected to be present in epidemic dynamics as well. Evidences of complexity in the COVID-19 epidemic dynamics have indeed been observed in a number of recent works, most noticeably in the form of a power-law behaviour in the early growth regime of case and death curves [2][3][4][5][6][7] , but also in the long-time asymptotic of the probability to become infected [8][9][10] . It has also been pointed out that such complex behaviour lies outside the range of applicability of standard SIR-type models, and a number of alternative dynamics have been suggested, such as the recent proposal of a random walk on a hierarchic landscape of social clusters [11][12][13] .…”

Universal epidemic curve for COVID-19 and its usage for forecasting

“…Refer to Fig. 2 and references [10,48,7,31,42,3] for more details on various power-law regimes of the epidemic curves. Rather than fitting with various power laws at different stages of the epidemic, we fit a large-degree polynomial that passes through the universal curve after the exponential regime.…”