{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T09:39:40Z","timestamp":1789551580816,"version":"build-2803163510"},"reference-count":31,"publisher":"The Royal Society","issue":"74","license":[{"start":{"date-parts":[[2012,3,22]],"date-time":"2012-03-22T00:00:00Z","timestamp":1332374400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/royalsociety.org\/journals\/ethics-policies\/data-sharing-mining\/"}],"content-domain":{"domain":["royalsocietypublishing.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2012,9,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>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.<\/jats:p>","DOI":"10.1098\/rsif.2011.0886","type":"journal-article","created":{"date-parts":[[2012,3,23]],"date-time":"2012-03-23T13:52:07Z","timestamp":1332510727000},"page":"2167-2180","update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":15,"title":["Multifractal signatures of infectious diseases"],"prefix":"10.1098","volume":"9","author":[{"given":"Amber M.","family":"Holdsworth","sequence":"first","affiliation":[{"name":"University of Alberta 1 , ,"},{"name":"Edmonton, Alberta, Canada 1 , ,"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nicholas K.-R.","family":"Kevlahan","sequence":"additional","affiliation":[{"name":"McMaster University 2 , ,"},{"name":"Hamilton, Ontario, Canada 2 , ,"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David J. D.","family":"Earn","sequence":"additional","affiliation":[{"name":"McMaster University 2 , ,"},{"name":"Hamilton, Ontario, Canada 2 , ,"},{"name":"McMaster University 3 , ,"},{"name":"Hamilton, Ontario, Canada 3 , ,"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"175","published-online":{"date-parts":[[2012,3,22]]},"reference":[{"key":"2026010517022274800_RSIF20110886C1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.vaccine.2006.07.039","article-title":"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","volume":"25","author":"Muller,","year":"2007","journal-title":"Vaccine"},{"key":"2026010517022274800_RSIF20110886C2","volume-title":"Stochastic population models in ecology and epidemiology","author":"Bartlett,","year":"1960"},{"key":"2026010517022274800_RSIF20110886C3","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1093\/oxfordjournals.aje.a121575","article-title":"Recurrent outbreaks of measles, chickenpox and mumps. I. Seasonal variation in contact rates","volume":"98","author":"London,","year":"1973","journal-title":"Am. J. Epidemiol."},{"key":"2026010517022274800_RSIF20110886C4","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1126\/science.287.5453.667","article-title":"A simple model for complex dynamical transitions in epidemics","volume":"287","author":"Earn,","year":"2000","journal-title":"Science"},{"key":"2026010517022274800_RSIF20110886C5","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1098\/rsif.2006.0192","article-title":"Stochastic amplification in epidemics","volume":"4","author":"Alonso,","year":"2007","journal-title":"J. R. Soc. Interface"},{"key":"2026010517022274800_RSIF20110886C6","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1038\/nature05638","article-title":"Seasonal dynamics of recurrent epidemics","volume":"446","author":"Stone,","year":"2007","journal-title":"Nature"},{"key":"2026010517022274800_RSIF20110886C7","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198545996.001.0001","volume-title":"Infectious diseases of humans: dynamics and control","author":"Anderson,","year":"1991"},{"key":"2026010517022274800_RSIF20110886C8","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1007\/BF01053588","article-title":"Singularity spectrum of fractal signals from wavelet analysis: exact results","volume":"70","author":"Bacry,","year":"1993","journal-title":"J. Stat. Phys."},{"key":"2026010517022274800_RSIF20110886C9","volume-title":"A wavelet tour of signal processing","author":"Mallat,","year":"1998"},{"key":"2026010517022274800_RSIF20110886C10","doi-asserted-by":"publisher","first-page":"971","DOI":"10.1137\/S0036141095283005","article-title":"Multifractal formalism for functions. II. Self-Similar functions","volume":"28","author":"Jaffard,","year":"1997","journal-title":"SIAM J. Math. Anal."},{"key":"2026010517022274800_RSIF20110886C11","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1038\/20924","article-title":"Multifractality in human heartbeat dynamics","volume":"399","author":"Ivanov,","year":"1999","journal-title":"Nature"},{"key":"2026010517022274800_RSIF20110886C12","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1186\/1743-0003-2-24","article-title":"Fractional Langevin model of gait variability","volume":"2","author":"West,","year":"2005","journal-title":"J. Neuroeng. Rehabil."},{"key":"2026010517022274800_RSIF20110886C13","first-page":"921","volume-title":"Multifractal analysis of electroencephalogram time series in humans","author":"Song,","year":"2005"},{"key":"2026010517022274800_RSIF20110886C14","doi-asserted-by":"publisher","first-page":"1195","DOI":"10.1016\/j.neuroimage.2004.03.007","article-title":"Wavelet-based multifractal analysis of fMRI time series","volume":"22","author":"Shimizu,","year":"2004","journal-title":"Neuroimage"},{"key":"2026010517022274800_RSIF20110886C15","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/j.autneu.2006.10.008","article-title":"Carvedilol can restore the multifractal properties of heart beat dynamics in patients with advanced congestive heart failure","volume":"132","author":"Chiu,","year":"2007","journal-title":"Auton. Neurosci. Basic Clin."},{"key":"2026010517022274800_RSIF20110886C16","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/978-3-540-78911-6_11","article-title":"The role of mathematical models in explaining recurrent outbreaks of infectious childhood diseases","volume":"1945","author":"Bauch,","year":"2008","journal-title":"Math. Epidemiol."},{"key":"2026010517022274800_RSIF20110886C17","doi-asserted-by":"publisher","first-page":"716","DOI":"10.1038\/414716a","article-title":"Travelling waves and spatial hierarchies in measles epidemics","volume":"414","author":"Grenfell,","year":"2001","journal-title":"Nature"},{"key":"2026010517022274800_RSIF20110886C18","first-page":"415","article-title":"A practical guide to wavelet analysis","volume":"4","author":"Torrence,","year":"1998","journal-title":"Bull. Am. Meteorol. Soc."},{"key":"2026010517022274800_RSIF20110886C19","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1061\/TACEAT.0006518","article-title":"Long-term storage capacity of reservoirs","volume":"116","author":"Hurst,","year":"1951","journal-title":"Trans. Am. Soc. Civ. Eng."},{"key":"2026010517022274800_RSIF20110886C20","article-title":"WaveLabe850","author":"Donoho,","year":"2007"},{"key":"2026010517022274800_RSIF20110886C21","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1109\/18.119727","article-title":"Singularity detection and processing with wavelets","volume":"38","author":"Mallat,","year":"1992","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2026010517022274800_RSIF20110886C22","article-title":"The International Infectious Disease Data Archive","author":"IIDDA"},{"key":"2026010517022274800_RSIF20110886C23","doi-asserted-by":"publisher","first-page":"1573","DOI":"10.1098\/rspb.2003.2410","article-title":"Transients and attractors in epidemics","volume":"270","author":"Bauch,","year":"2003","journal-title":"Proc. R. Soc. Lond. B"},{"key":"2026010517022274800_RSIF20110886C24","volume-title":"The mathematical theory of infectious diseases and its applications","author":"Bailey,","year":"1975","edition":"2nd edn."},{"key":"2026010517022274800_RSIF20110886C25","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1007\/978-3-642-61850-5_39","article-title":"Relationships between stochastic and deterministic population models","volume":"38","author":"Kurtz,","year":"1980","journal-title":"Lect. Notes Biomath."},{"key":"2026010517022274800_RSIF20110886C26","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1098\/rspa.1927.0118","article-title":"A contribution to the mathematical theory of epidemics","volume":"115","author":"Kermack,","year":"1927","journal-title":"Proc. R. Soc. Lond. A"},{"key":"2026010517022274800_RSIF20110886C27","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1016\/j.tpb.2007.04.004","article-title":"Epidemiological effects of seasonal oscillations in birth rates","volume":"72","author":"He,","year":"2007","journal-title":"Theor. Popul. Biol."},{"key":"2026010517022274800_RSIF20110886C28","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1090\/pcms\/014\/05","article-title":"Mathematical epidemiology of infectious diseases","volume-title":"Mathematical biology","author":"Earn,","year":"2009"},{"key":"2026010517022274800_RSIF20110886C29","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1016\/0021-9991(76)90041-3","article-title":"A general method for numerically simulating the stochastic time evolution of coupled chemical reactions","volume":"22","author":"Gillespie,","year":"1976","journal-title":"J. Comput. Phys."},{"key":"2026010517022274800_RSIF20110886C30","doi-asserted-by":"publisher","first-page":"968","DOI":"10.1126\/science.286.5441.968","article-title":"Opposite patterns of synchrony in sympatric disease metapopulations","volume":"286","author":"Rohani,","year":"1999","journal-title":"Science"},{"key":"2026010517022274800_RSIF20110886C31","doi-asserted-by":"publisher","first-page":"506","DOI":"10.1038\/nature10549","article-title":"A draft genome of Yersinia pestis from victims of the Black Death","volume":"478","author":"Bos,","year":"2011","journal-title":"Nature"}],"container-title":["Journal of The Royal Society Interface"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rsif.2011.0886","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/full-xml\/10.1098\/rsif.2011.0886","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/rsif\/article-pdf\/9\/74\/2167\/3846\/rsif.2011.0886.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/royalsocietypublishing.org\/rsif\/article-pdf\/9\/74\/2167\/3846\/rsif.2011.0886.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T22:04:37Z","timestamp":1767650677000},"score":1,"resource":{"primary":{"URL":"https:\/\/royalsocietypublishing.org\/rsif\/article\/9\/74\/2167\/247\/Multifractal-signatures-of-infectious"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3,22]]},"references-count":31,"journal-issue":{"issue":"74","published-print":{"date-parts":[[2012,9,7]]}},"URL":"https:\/\/doi.org\/10.1098\/rsif.2011.0886","relation":{},"ISSN":["1742-5689","1742-5662"],"issn-type":[{"value":"1742-5689","type":"print"},{"value":"1742-5662","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3,22]]},"assertion":[{"value":"2011-12-16","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-03-02","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-03-22","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}