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 April 20, 2020. We observe that China, South Korea, Australia, Hong Kong, and Switzerland have flattened their infection curves. For these nations, the total number of infected individuals (I(t)) exhibits a succession of exponential growth and power-law growth (t2,t,{surd}t in sequence) before flattening of the curve. USA, Italy, UK, France, Spain, Germany, Belgium, Israel, Netherlands, India, and Sri Lanka have reached up to the linear growth (I(t) [~] t), but they are yet to flatten their curves. Russia and Singapore are still in the exponential growth regime. Such features of I(t) curves could be used for understanding and forecast of the epidemic evolution. Besides this detailed analysis, we compare the predictions of an extended SEIR model and a delay differential equation-based model with the reported infection data, and observed a general agreement between them.

[1]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[2]  Daryl J. Daley,et al.  Epidemic Modelling: An Introduction , 1999 .

[3]  J. Westerink,et al.  Modeling the physics of storm surges , 2008 .

[4]  M. Newman.  The physics of networks , 2008 .

[5]  Computational epidemiology , 2013, CACM.

[6]  M. Höhle.  Infectious Disease Modelling , 2016 .

[7]  R. Sarpong,et al.  Bio-inspired synthesis of xishacorenes A, B, and C, and a new congener from fuscol† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c9sc02572c , 2019, Chemical science.

[8]  O. Bjørnstad.  Epidemics: Models and Data using R , 2018 .

[9]  W. Hager,et al.  and s , 2019, Shallow Water Hydraulics.

[10]  B. Blasius.  Power-law distribution in the number of confirmed COVID-19 cases , 2020, Chaos.

[11]  N. Arinaminpathy,et al.  Prudent public health intervention strategies to control the coronavirus disease 2019 transmission in India: A mathematical model-based approach , 2020, The Indian journal of medical research.

[12]  Alexis Akira Toda,et al.  On the emergence of a power law in the distribution of COVID-19 cases , 2020, Physica D: Nonlinear Phenomena.

[13]  G. Pandey,et al.  SEIR and Regression Model based COVID-19 outbreak predictions in India , 2020, medRxiv.

[14]  Cui Meng,et al.  Propagation analysis and prediction of the COVID-19 , 2020, Infectious Disease Modelling.

[15]  Regis W. Anne,et al.  ARIMA modelling of predicting COVID-19 infections , 2020, medRxiv.

[16]  Liangrong Peng,et al.  Epidemic analysis of COVID-19 in China by dynamical modeling , 2020, medRxiv.

[17]  Momentum managing epidemic spread and Bessel functions☆ , 2020, Chaos, Solitons & Fractals.

[18]  D. Sornette,et al.  Generalized logistic growth modeling of the COVID-19 outbreak in 29 provinces in China and in the rest of the world , 2020, medRxiv.

[19]  Ruiyun Li,et al.  Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV-2) , 2020, Science.

[20]  Etienne Cheynet,et al.  Generalized SEIR Epidemic Model (fitting and computation) , 2020 .

[21]  P. Klepac,et al.  Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts , 2020, The Lancet Global Health.

[22]  Eduardo L. Brugnago,et al.  Strong correlations between power-law growth of COVID-19 in four continents and the inefficiency of soft quarantine strategies , 2020, Chaos.

[23]  Pankaj Mehta,et al.  Data-driven modeling reveals a universal dynamic underlying the COVID-19 pandemic under social distancing , 2020, medRxiv.

[24]  R. Rand,et al.  Self-burnout - a new path to the end of COVID-19 , 2020, medRxiv.

[25]  S. Deb,et al.  A time series method to analyze incidence pattern and estimate reproduction number of COVID-19 , 2020, 2003.10655.

[26]  Junling Ma.  Estimating epidemic exponential growth rate and basic reproduction number , 2020, Infectious Disease Modelling.

[27]  D. Wodarz,et al.  Patterns of the COVID19 epidemic spread around the world: exponential vs power laws , 2020, medRxiv.

[28]  R. Ranjan.  Estimating the Final Epidemic Size for COVID-19 Outbreak using Improved Epidemiological Models , 2020, medRxiv.

[29]  H. Singer,et al.  The COVID-19 pandemic: growth patterns, power law scaling, and saturation , 2020, Physical biology.

[30]  P. Piro,et al.  Investigating a Serious Challenge in the Sustainable Development Process: Analysis of Confirmed cases of COVID-19 (New Type of Coronavirus) Through a Binary Classification Using Artificial Intelligence and Regression Analysis , 2020, Sustainability.

[31]  N. Arinaminpathy,et al.  Prudent public health intervention strategies to control the coronavirus disease 2019 transmission in India: A mathematical model-based approach , 2020, The Indian journal of medical research.

[32]  R. Ziff,et al.  Fractal kinetics of COVID-19 pandemic , 2020, medRxiv.

[33]  M. Kröger,et al.  Covid-19 Predictions Using a Gauss Model, Based on Data from April 2 , 2020, Physics.

[34]  COVID-19 Pandemic: Power Law Spread and Flattening of the Curve , 2020, Transactions of the Indian National Academy of Engineering.

[35]  Jessica T Davis,et al.  The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak , 2020, Science.

[36]  Soumyadeep Bhattacharya,et al.  A minimal and adaptive prediction strategy for critical resource planning in a pandemic , 2020, medRxiv.

[37]  Marta Giovanetti,et al.  Application of the ARIMA model on the COVID-2019 epidemic dataset , 2020, Data in Brief.

[38]  Youjin Deng,et al.  Scaling features in the spreading of COVID-19 , 2020, 2002.09199.

[39]  X. Rodó,et al.  A modified SEIR model to predict the COVID-19 outbreak in Spain and Italy: Simulating control scenarios and multi-scale epidemics , 2020, Results in Physics.

[40]  Transmission Dynamics of 2019-nCoV in Malaysia , 2020, medRxiv.

[41]  F. D. de Castro.  Modelling of the second (and subsequent) waves of the coronavirus epidemic. Spain and Germany as case studies , 2020, medRxiv.

[42]  P. Alam.  ‘A’ , 2021, Composites Engineering: An A–Z Guide.

[43]  P. Alam,et al.  R , 1823, The Herodotus Encyclopedia.