An analysis of COVID-19 spread based on fractal interpolation and fractal dimension

Abstract The present paper proposes a reconstruction of the epidemic curves from the fractal interpolation point of view. Looking at the epidemic curves as fractal structures might be an efficient way to retrieve missing pieces of information due to insufficient testing and predict the evolution of the disease. A fractal approach of the epidemic curve can contribute to the assessment and modeling of other epidemics. On the other hand, we have considered the spread of the epidemic in countries like Romania, Italy, Spain, and Germany and analyzed the spread of the disease in those countries based on their fractal dimension.

[1]  F. Piazza,et al.  Analysis and forecast of COVID-19 spreading in China, Italy and France , 2020, Chaos, Solitons & Fractals.

[2]  Paul J. Birrell,et al.  Evidence Synthesis for Stochastic Epidemic Models. , 2017, Statistical science : a review journal of the Institute of Mathematical Statistics.

[3]  J. Rocklöv,et al.  The reproductive number of COVID-19 is higher compared to SARS coronavirus , 2020, Journal of travel medicine.

[4]  C. Anastassopoulou,et al.  Data-based analysis, modelling and forecasting of the COVID-19 outbreak , 2020, medRxiv.

[5]  Pramit Ghosh,et al.  Increased Detection coupled with Social Distancing and Health Capacity Planning Reduce the Burden of COVID-19 Cases and Fatalities: A Proof of Concept Study using a Stochastic Computational Simulation Model , 2020, medRxiv.

[6]  P. Massopust.  Fractal functions and their applications , 1997 .

[7]  E. Holmes,et al.  The proximal origin of SARS-CoV-2 , 2020, Nature Medicine.

[8]  C W Potter,et al.  A history of influenza , 2001, Journal of applied microbiology.

[9]  M. Sebastián,et al.  Fractal Interpolation Functions: A Short Survey , 2014 .

[10]  Kai Zhao,et al.  A pneumonia outbreak associated with a new coronavirus of probable bat origin , 2020, Nature.

[11]  Tao Zhang,et al.  Pangolin homology associated with 2019-nCoV , 2020, bioRxiv.

[12]  Michael F. Barnsley,et al.  Fractal functions and interpolation , 1986 .

[13]  G. Kroemer,et al.  Coronavirus infections: Epidemiological, clinical and immunological features and hypotheses , 2020, Cell stress.

[15]  Laura Matrajt,et al.  Evaluating the Effectiveness of Social Distancing Interventions to Delay or Flatten the Epidemic Curve of Coronavirus Disease , 2020, Emerging infectious diseases.

[16]  Michael F. Barnsley,et al.  Hidden variable fractal interpolation functions , 1989 .

[17]  P. Massopust.  Fractal Functions, Fractal Surfaces, and Wavelets , 1995 .

[18]  J. Nygård,et al.  Fractal analysis of time series in epidemiology: Is there information hidden in the noise? , 2009 .

[19]  Vasileios Drakopoulos,et al.  Curve Fitting by Fractal Interpolation , 2008, Trans. Comput. Sci..

[20]  P. Klepac,et al.  Early dynamics of transmission and control of COVID-19: a mathematical modelling study , 2020, The Lancet Infectious Diseases.

[21]  Delfim F. M. Torres,et al.  Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan , 2020, Chaos, Solitons & Fractals.

[23]  A. Schuchat,et al.  COVID-19: towards controlling of a pandemic , 2020, The Lancet.

[24]  Michael F. Barnsley,et al.  The calculus of fractal interpolation functions , 1989 .

[25]  Timothy F. Leslie,et al.  Complexity of the Basic Reproduction Number (R0) , 2019, Emerging infectious diseases.

[26]  Joseph Dureau,et al.  Capturing the time-varying drivers of an epidemic using stochastic dynamical systems. , 2012, Biostatistics.

[27]  Swapan Kumar Nandi,et al.  A model based study on the dynamics of COVID-19: Prediction and control , 2020, Chaos, Solitons & Fractals.

[28]  Michael F. Barnsley,et al.  Fractals everywhere , 1988 .

[29]  G. D. Barmparis,et al.  Estimating the infection horizon of COVID-19 in eight countries with a data-driven approach , 2020, Chaos, Solitons & Fractals.

[30]  Andrzej Kloczkowski,et al.  Identification of an Epidemiological Model to Simulate the COVID-19 Epidemic Using Robust Multiobjective Optimization and Stochastic Fractal Search , 2020, Comput. Math. Methods Medicine.