Multifractal signatures of infectious diseases

Journal of the Royal Society Interface

Volumn 9, Issue 74, 2012, Pages 2167-2180

  Holdsworth, Amber M ^a   Kevlahan, Nicholas K R ^b   Earn, David J D ^b,c  

^a UNIVERSITY OF ALBERTA   (Canada)

^b MCMASTER UNIVERSITY   (Canada)

^c MCMASTER UNIVERSITY   (Canada)

Author keywords

Infectious disease; Multifractal; Wavelet

Indexed keywords

ANIMALS; DISEASES; EPIDEMIOLOGY; STOCHASTIC SYSTEMS; TIME SERIES;

CHILDHOOD DISEASE; EPIDEMIC MODELS; INFECTIOUS DISEASE; MONOFRACTAL STRUCTURE; MULTI FRACTALS; MULTI-SCALE STRUCTURES; SCALING FUNCTIONS; SEIR EPIDEMIC MODELS; SIMULATED DATA; SUSCEPTIBLE-EXPOSED-INFECTIOUS-RECOVERED; TIME-SERIES DATA; WAVELET; WAVELET TRANSFORM MAXIMUM MODULUS; WHOOPING COUGH;

FRACTALS;

ARTICLE; CHICKENPOX; INCIDENCE; MEASLES; PERTUSSIS; RUBELLA; TIME SERIES ANALYSIS; VACCINATION; WAVELET ANALYSIS; WAVELET TRANSFORM MAXIMUM MODULUS;

RUBELLA;

EID: 84866146573     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2011.0886     Document Type: Article

References (31)

1. Muller, C. P., Kremer, J. R., Best, J. M., Dourado, I., Triki, H. & Reef, S. 2007 Reducing global disease burden of measles and rubella: report of the WHO Steering Committee on research related to measles and rubella vaccines and vaccination, 2005. Vaccine 25, 1-9. (doi:10.1016/j.vaccine.2006.07.039)
2. Bartlett, M. S. 1960 Stochastic population models in ecology and epidemiology, vol. 4. Methuen's Monographs on Applied Probability and Statistics. London, UK: Spottiswoode, Ballantyne & Co. Ltd.
3. London, W. & Yorke, J. A. 1973 Recurrent outbreaks of measles, chickenpox and mumps. I. Seasonal variation in contact rates. Am. J. Epidemiol. 98, 453-468.
4. Earn, D. J. D., Rohani, P., Bolker, B. M. & Grenfell, B. T. 2000 A simple model for complex dynamical transitions in epidemics. Science 287, 667-670. (doi:10.1126/science.287.5453.667)
5. Alonso, D., McKane, A. J. & Pascual, M. 2007 Stochastic amplification in epidemics. J. R. Soc. Interface 4, 575-582. (doi:10.1098/ rsif.2006.0192)
6. Stone, L., Olinky, R. & Huppert, A. 2007 Seasonal dynamics of recurrent epidemics. Nature 446, 533-536. (doi:10.1038/nature05638)
7. Anderson, R. M. & May, R. M. 1991 Infectious diseases of humans: dynamics and control. Oxford, UK: Oxford University Press.
8. Bacry, E., Muzy, J. & Arneodo, A. 1993 Singularity spectrum of fractal signals from wavelet analysis: exact results. J. Stat. Phys. 70, 635-674. (doi:10.1007/BF01053588)
9. Mallat, S. 1998 A wavelet tour of signal processing. Burlington, MA: Academic Press.
10. Jaffard, S. 1997 Multifractal formalism for functions. II. Self-Similar functions. SIAM J. Math. Anal. 28, 971-998. (doi:10.1137/S0036141095283005)
11. Ivanov, P. C., Amaral, L. A., Goldberger, A. L., Havlin, S., Rosenblum, M. G., Struzik, Z. R. & Stanley, H. E. 1999 Multifractality in human heartbeat dynamics. Nature 399, 461-465. (doi:10.1038/20924)
12. West, B. J. & Latka, M. 2005 Fractional Langevin model of gait variability. J. Neuroeng. Rehabil. 2, 24-33. (doi:10.1186/1743-0003-2-24)
13. Song, I. H., Lee, S. M., Kim, I. Y., Lee, D. S. & Kim, S. I. 2005 In Multifractal analysis of electroencephalogram time series in humans. Lecture Notes in Computer Science, pp. 921-926. Berlin, Germany: Springer.
14. Shimizu, Y., Barth, M., Windischberger, C., Mose, E. & Thurner, S. 2004 Wavelet-based multifractal analysis of fMRI time series. Neuroimage 22, 1195-202. (doi:10.1016/j.neuroimage.2004.03.007)
15. Chiu, K. M., Chan, H. L., Chu, S. H. & Lin, T. Y. 2007 Carvedilol can restore the multifractal properties of heart beat dynamics in patients with advanced congestive heart failure. Auton. Neurosci. Basic Clin. 132, 76-80. (doi:10.1016/j.autneu.2006.10.008)
16. Bauch, C. T. 2008 The role of mathematical models in explaining recurrent outbreaks of infectious childhood diseases. Math. Epidemiol. 1945, 297-319. (doi:10.1007/978-3-540-78911-6-11)
17. Grenfell, B. T., Kappey, J. & Bjornstad, O. N. 2001 Travelling waves and spatial hierarchies in measles epidemics. Nature 414, 716-723. (doi:10.1038/414716a)
18. Torrence, C. & Compo, G. P. 1998 A practical guide to wavelet analysis. Bull. Am. Meteorol. Soc. 4, 415-447. See http://www.inference.phy.cam. ac.uk/mackay/PhD.html.
19. Hurst, H. E. 1951 Long-term storage capacity of reservoirs. Trans. Am. Soc. Civ. Eng. 116, 770-808.
20. Donoho, D., Maleki, A. & Shahram, M. 2007 Wave-Labe850. See www-stat.stanford.edu/wavelab.
21. Mallat, S. & Hwang, W. L. 1992 Singularity detection and processing with wavelets. IEEE Trans. Inf. Theory 38, 617-643. (doi:10.1109/18.119727)
22. IIDDA. The International Infectious Disease Data Archive. See http://iidda.mcmaster.ca.
23. Bauch, C. & Earn, D. 2003 Transients and attractors in epidemics. Proc. R. Soc. Lond. B 270, 1573-1578. (doi:10.1098/ rspb.2003.2410)
24. Bailey, N. T. J. 1975 The mathematical theory of infectious diseases and its applications, 2nd edn. New York, NY: Hafner Press.
25. Kurtz, T. G. 1980 Relationships between stochastic and deterministic population models. Lect. Notes Biomath. 38, 449-467. (doi:10.1007/978-3-642- 61850-5-39)
26. Kermack, W. O. & McKendrick, A. G. 1927 A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. A 115, 700-721. (doi:10.1098/rspa.1927.0118)
27. He, D. & Earn, D. J. D. 2007 Epidemiological effects of seasonal oscillations in birth rates. Theor. Popul. Biol. 72, 274-291. (doi:10.1016/j.tpb.2007.04.004)
28. Earn, D. J. D. 2009 Mathematical epidemiology of infectious diseases. In Mathematical biology, vol. 14 (eds M. A. Lewis, M. A. J. Chaplain, J. P. Keener & P. K. Maini), pp. 151-186. Providence, RI: IAS/Park City, Mathematics Series American Mathematical Society.
29. Gillespie, D. T. 1976 A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403-434. (doi:10.1016/0021-9991(76)90041-3)
30. Rohani, P., Earn, D. & Grenfell, B. 1999 Opposite patterns of synchrony in sympatric disease metapopulations. Science 286, 968-971. (doi:10.1126/science.286.5441.968)
31. Bos, K. I. et al. 2011 A draft genome of Yersinia pestis from victims of the Black Death. Nature 478, 506-510. (doi:10.1038/ nature10549)