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Multifractal signatures of infectious diseases
Amber M Holdsworth1, Nicholas K-R Kevlahan, David J D Earn
1Department of Earth and Atmospheric Sciences, University of Alberta, Edmonton, Alberta, Canada.
Abstract:
Incidence of infection time-series data for the childhood diseases measles, chicken pox, rubella and whooping cough are described in the language of multifractals. We explore the potential of using the wavelet transform maximum modulus (WTMM) method to characterize the multiscale structure of the observed time series and of simulated data generated by the stochastic susceptible-exposed-infectious-recovered (SEIR) epidemic model. The singularity spectra of the observed time series suggest that each disease is characterized by a unique multifractal signature, which distinguishes that particular disease from the others. The wavelet scaling functions confirm that the time series of measles, rubella and whooping cough are clearly multifractal, while chicken pox has a more monofractal structure in time. The stochastic SEIR epidemic model is unable to reproduce the qualitative singularity structure of the reported incidence data: it is too smooth and does not appear to have a multifractal singularity structure. The precise reasons for the failure of the SEIR epidemic model to reproduce the correct multiscale structure of the reported incidence data remain unclear.
Insights
Childhood infection time-series data exhibit unique multifractal signatures. The wavelet transform maximum modulus (WTMM) method revealed distinct patterns for measles, rubella, and whooping cough, unlike chickenpox. The SEIR model failed to replicate these complex multifractal structures.
Area of Science:
- Epidemiology
- Complex Systems Analysis
- Time Series Analysis
Background:
- Childhood infectious diseases like measles, chickenpox, rubella, and whooping cough generate time-series data.
- Understanding the complex dynamics and multiscale structures within these incidence data is crucial for epidemiological modeling.
Purpose of the Study:
- To characterize the multiscale structure of childhood disease incidence time series using multifractal analysis.
- To compare the multifractal properties of real disease data with simulations from the susceptible-exposed-infectious-recovered (SEIR) epidemic model.
Main Methods:
- Application of the wavelet transform maximum modulus (WTMM) method to analyze time-series data.
- Calculation of singularity spectra to identify multifractal characteristics.
- Comparison of observed disease data with data simulated using a stochastic SEIR model.
Main Results:
- Each childhood disease (measles, rubella, whooping cough) displayed a unique multifractal signature.
- Measles, rubella, and whooping cough time series demonstrated clear multifractal behavior, while chickenpox showed a more monofractal structure.
- The stochastic SEIR model failed to reproduce the observed multifractal singularity structure, producing overly smooth data.
Conclusions:
- Multifractal analysis, particularly using WTMM, can effectively differentiate between the temporal dynamics of various childhood infectious diseases.
- Current stochastic SEIR models may not fully capture the complex multiscale phenomena present in real-world epidemic incidence data.
- Further research is needed to understand why the SEIR model fails to replicate the observed multifractal properties.
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