True epidemic growth construction through harmonic analysis

Abstract In this paper, we have proposed a two-phase procedure (combining discrete graphs and wavelets) for constructing true epidemic growth. In the first phase, a graph-theory-based approach was developed to update partial data available and in the second phase, we used this partial data to generate plausible complete data through wavelets. We have provided two numerical examples. This procedure is novel and implementable and adaptable to machine learning modeling framework.

[1]  D. Earn,et al.  Transients and attractors in epidemics , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[2]  James S. Walker Fourier Analysis and Wavelet Analysis , 1998 .

[3]  R. Strichartz How to Make Wavelets , 1993 .

[4]  Chris T. Bauch,et al.  The Role of Mathematical Models in Explaining Recurrent Outbreaks of Infectious Childhood Diseases , 2008 .

[5]  H. E. Soper The Interpretation of Periodicity in Disease Prevalence , 1929 .

[6]  M. Bartlett Measles Periodicity and Community Size , 1957 .

[7]  B T Grenfell,et al.  Oscillatory fluctuations in the incidence of infectious disease and the impact of vaccination: time series analysis , 1984, Journal of Hygiene.

[8]  Mario Chavez,et al.  Wavelet analysis in ecology and epidemiology: impact of statistical tests , 2014, Journal of The Royal Society Interface.

[9]  G. Weiss,et al.  A First Course on Wavelets , 1996 .

[10]  R. May,et al.  Infectious Diseases of Humans: Dynamics and Control , 1991, Annals of Internal Medicine.

[11]  Arni S. R. Srinivasa Rao,et al.  Understanding Theoretically The Impact of Reporting of Disease Cases in Epidemiology , 2012, 1202.2688.

[12]  D. Earn,et al.  Interepidemic Intervals in Forced and Unforced SEIR Models , 2022 .

[13]  Adam Kleczkowski,et al.  Seasonality and extinction in chaotic metapopulations , 1995, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[14]  O. Bjørnstad,et al.  Travelling waves and spatial hierarchies in measles epidemics , 2001, Nature.

[15]  Steven G. Krantz,et al.  A Panorama of Harmonic Analysis , 1999 .