Emerging Polynomial Growth Trends in COVID-19 Pandemic Data and Their Reconciliation with Compartment Based Models

Abstract

We study the reported data from the COVID-19 pandemic outbreak in January -May 2020 in 119 countries. We observe that the time series of active cases in individual countries (the difference of the total number of confirmed infections and the sum of the total number of reported deaths and recovered cases) display a strong agreement with polynomial growth and at a later epidemic stage also with a combined polynomial growth with exponential decay. Our results are also formulated in terms of compartment type mathematical models of epidemics. Within these models the universal scaling characterizing the observed regime in an advanced epidemic stage can be interpreted as an algebraic decay of the relative reproduction number R 0 as T M /t, where T M is a constant and t is the duration of the epidemic outbreak. We show how our findings can be applied to improve predictions of the reported pandemic data and estimate some epidemic paramters. Note that although the model shows a good agreement with the reported data we do not make any claims about the real size of the pandemics as the relation of the observed reported data to the total number of infected in the population is still unknown.

Contact network models matching the dynamics of the COVID-19 spreading

“…Note that the result obtained in [20] includes power-law growth combined with exponential decay. While this exponential decay term can be conveniently used to fit the slowing epidemic data [28], the source of this decay is the shrinking size of the susceptible population which, fortunately, is not a significant effect for COVID-19 which has yet affected a minor fraction of the world's population. In the scope of fitting the COVID-19 data, the exponential decay term has to be thus viewed as phenomenological.…”

“…As we have already mentioned, empirical dynamics of the COVID-19 epidemic has been already studied in a great number of works [14][15][16][17][18][19][26][27][28]. To provide a direct motivation for our study of power-law patterns in epidemic dynamics, we offer here a simple visualization of empirical data on COVID-19 fatalities in Switzerland.…”

“…We use here the model introduced in [23] where N nodes form a The number of COVID-19 fatalities in Switzerland (CH) and three mostaffected cantons (Vaud, VD, Ticino, TI, and Geneva, GE) vs the number of days since the first fatality. See [14][15][16][17][18][19][26][27][28] for further empirical evidence of power-law epidemic growth.…”

“…Our results thus provide an indirect way of probing the structure of actual contact networks over which the virus spreads, as well as suggestions for making these networks less permissible to the virus. Note that we purposely avoid the question of epidemic predictions which has been addressed using phenomenological fits [26][27][28] and extensive agent-based models [29] elsewhere.…”