Fractal Signatures in Epidemic Curves – Real Data Analysis
Year: 2025
Type: article
Abstract: Background: Epidemic time‑series often display complex, self‑similar patterns consistent with fractal and long‑memory dynamics. Understanding these patterns provides insight into the persistence and predictability of disease spread. Objective: To quantify fractal characteristics in real epidemic curves using global COVID‑19 surveillance data. Methods: Johns Hopkins CSSE COVID‑19 daily confirmed case counts were analyzed for each country. For each series, Hurst exponent (H), fractal dimension (D = 2 − H), Detrended Fluctuation Analysis (DFA), Lyapunov exponent, and lag‑1 autocorrelation (AC1) were computed. Results: Most countries exhibited H > 0.5, indicating persistence and long‑range dependence. Guinea, Ghana, and Congo (Brazzaville) showed the highest H (~0.91). Conclusion: Epidemic curves exhibit fractal persistence suggestive of self‑organized criticality; recognizing such properties could improve modeling and control strategies. Introduction Fractal geometry and non‑linear dynamics have been increasingly applied to biological and epidemiological processes to describe scale‑invariant behavior and long‑range correlations. The Hurst exponent (H) quantifies long‑memory, while fractal dimension (D = 2 − H) expresses structural complexity. During COVID‑19, epidemic curves displayed recurring waves that may reflect underlying fractal organization. This analysis explores real‑world epidemic data to characterize such properties. Methods Data were obtained from the Johns Hopkins University CSSE COVID‑19 dataset (global daily confirmed cases). Time‑series for each country were cleaned, aggregated, and transformed into daily increments. Fractal measures were computed as follows: Hurst exponent using rescaled‑range analysis (Hurst 1951); Detrended Fluctuation Analysis (Peng et al., 1994); Lyapunov exponent and autocorrelation using non‑linear dynamics toolkit (Nolds). Values of H > 0.5 indicate persistence (positive correlation of increments); H < 0.5 indicates anti‑persistence. Results A total of 201 country‑level series were analyzed. Top ten locations by Hurst exponent are summarized below. disease location N Hurst FractalDim DFA Lyapunov AC1 COVID-19 Guinea 1092 0.9141 1.0859 0.9828 0.0364 0.3685 COVID-19 Ghana 1091 0.913 1.087 0.9354 0.0473 0.395 COVID-19 Congo (Brazzaville) 1090 0.9113 1.0887 0.6121 0.0355 -0.0526 COVID-19 Guinea-Bissau 1080 0.8981 1.1019 0.895 0.0185 0.2123 COVID-19 Nicaragua 1086 0.898 1.102 0.3575 0.0678 -0.0382 COVID-19 Somalia 1089 0.8834 1.1166 0.5867 0.0214 0.074 COVID-19 Gabon 1091 0.8816 1.1184 0.7649 0.0487 -0.014 COVID-19 Palau 565 0.876 1.124 1.0035 -0.0137 0.4637 COVID-19 Sudan 1091 0.8725 1.1275 0.8241 0.0013 0.3256 COVID-19 Haiti 1085 0.8715 1.1285 1.1255 0.0002 0.6384 Table 1 – Top 10 countries by Hurst exponent (H) computed from COVID‑19 time‑series. Figure 1 – Top Hurst exponents across countries (COVID‑19). Figure 2 – COVID‑19 daily/weekly cases – India. Figure 3 – COVID‑19 daily/weekly cases – United States. Figure 4 – COVID‑19 daily/weekly cases – Brazil. Figure 5 – COVID‑19 daily/weekly cases – France. Figure 6 – COVID‑19 daily/weekly cases – Germany. Figure 7 – Simplified PRISMA flow diagram. Discussion The consistently high Hurst values (> 0.8) observed across countries indicate strong persistence in epidemic dynamics. This suggests that increments in case counts are not independent but retain memory of prior states, reflecting long‑range temporal correlations. Such behavior aligns with the concept of self‑organized criticality in complex adaptive systems. Differences between nations may relate to intervention timing, reporting practices, and network connectivity. DFA and Lyapunov analyses further support the presence of deterministic chaos and fractal scaling in transmission. Understanding these signatures can improve forecasting: persistent systems respond slowly to control measures, requiring early and sustained interventions. Anti‑persistent or chaotic systems may oscillate rapidly, demanding flexible, adaptive responses. Conclusion Real epidemic curves of COVID‑19 exhibit fractal and long‑memory behavior. Quantitative fractal metrics provide complementary tools to conventional compartmental models, offering deeper insight into epidemic predictability and control. References [1] Mandelbrot BB. *The Fractal Geometry of Nature.* New York: W.H. Freeman; 1982. [2] Hurst HE. Long‑term storage capacity of reservoirs. *Transactions of the American Society of Civil Engineers.* 1951;116:770‑808. [3] Peng C‑K, Buldyrev SV, Havlin S, Simons M, Stanley HE, Goldberger AL. Mosaic organization of DNA nucleotides. *Phys Rev E.* 1994;49(2):1685‑1689. [4] Costa M, Goldberger AL, Peng C‑K. Multiscale entropy analysis of complex physiologic time series. *Phys Rev Lett.* 2002;89(6):068102. [5] Johns Hopkins University Center for Systems Science and Engineering (CSSE). COVID‑19 Data Repository. https://github.com/CSSEGISandData/COVID‑19. [6] World Health Organization (WHO). Coronavirus disease (COVID‑19) dashboard data. 2021. https://data.who.int. Title: Fractal Signatures in Epidemic Curves – Real Data Analysis Dr. Siddalingaiah H. S.Professor of Community MedicineShridevi Institute of Medical Sciences & Research Hospital, Tumkur, Karnataka, India
Author: H.S., Siddalingaiah
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7104051045
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