Temporal Scaling Behavior of Avian Influenza A (H5N1): The Multifractal Detrended Fluctuation Analysis

References

• Adene , D. and Oguntad , A. 2006 . The structure and importance of the commercial and village based poultry industry in Nigeria , Rome : Food and Agriculture Organization of the United Nations .
   Google Scholar
• Alexander , D. J. 2007 . An overview of the epidemiology of avian influenza . Vaccine , 25 ( 30 ) : 5637 – 44 .
   PubMed Web of Science ®Google Scholar
• Alvarez-Ramirez , J. , Alvarez , J. , Dagdug , L. , Rodriguez , E. and Echeverria , J. C. 2008 . Long-term memory dynamics of continental and oceanic monthly temperatures in the recent 125 years . Physica A: Statistical Mechanics and Its Applications , 387 ( 14 ) : 3629 – 40 .
   Google Scholar
• Anh , V. , Lam , K. , Leung , Y. and Tieng , Q. 2000 . Multifractal analysis of Hong Kong air quality data . Environmetrics , 11 : 139 – 49 .
   Google Scholar
• Anh , V. , Yu , Z.-G. and Wanliss , J. A. 2007 . Analysis of global geomagnetic variability . Nonlinear Processes in Geophysics , 14 ( 6 ) : 701 – 08 .
   Google Scholar
• Aubin , J.-T. , Zebi , S. , Balish , A. , Banks , J. , Bhat , N. , Bright , R. A. Bronw , L. 2005 . Evolution of H5N1 avian influenza viruses in Asia . Emerging Infectious Diseases , 11 ( 10 ) : 1515 – 21 .
   PubMedGoogle Scholar
• Benson , D. A. , Karsch-Mizrachi , I. , Lipman , D. J. , Ostell , J. and Wheeler , D. L. 2006 . GenBank . Nucleic Acids Research , 34 ( D16 )
   Google Scholar
• Carrel , M. , Emch , M. , Jobe , R. , Moody , A. and Wan , X-F. 2010 . Spatio-temporal structure of molecular evolution of H5N1 highly pathogenic avian influenza in Vietnam . PLoS One , 5 : e86311 – e86319 .
   Google Scholar
• Cattoli , G. , Monne , I. , Fusaro , A. , Joannis , T. M. , Lombin , L. H. , Aly , M. M. Arafa , A. S. 2009 . Highly pathogenic avian influenza virus subtype H5N1 in Africa: A comprehensive phylogenetic analysis and molecular characterization of isolates . PLoS ONE , 4 ( 3 ) : e4842
   Google Scholar
• Cecchi , G. , Ilemobade , A. , Brun , Y. L. , Hogerwerf , L. and Slingenbergh , J. 2008 . Agro-ecological features of the introduction and spread of the highly pathogenic avian influenza (HPAI) H5N1 in northern Nigeria . Geospatial Health , 3 ( 1 ) : 7 – 16 .
   PubMedGoogle Scholar
• Chaichoune , K. , Wiriyarat , W. , Thitithanyanont , A. , Phonarknguen , R. , Sariya , L. , Suwanpakdee , S. Noimor , T. 2009 . Indigenous sources of 2007–2008 H5N1 avian influenza outbreaks in Thailand . Journal of General Virology , 90 ( 1 ) : 216 – 22 .
   PubMedGoogle Scholar
• Chen , H. , Smith , G. J. D. , Li , K. S. , Wang , J. , Fan , X. H. , Rayner , J. M. Vijaykrishna , D. 2006 . Establishment of multiple sublineages of H5N1 influenza virus in Asia: Implications for pandemic control . Proceedings of the National Academy of Sciences USA , 103 ( 8 ) : 2845 – 50 .
   PubMed Web of Science ®Google Scholar
• Chen , H. , Smith , G. J. D. , Zhang , S. Y. , Qin , K. , Wang , J. , Li , K. S. , Webster , R. G. , Peiris , J. S. M. and Guan , Y. 2005 . Avian flu: H5N1 virus outbreak in migratory waterfowl . Nature , 436 ( 7048 ) : 191 – 92 .
   PubMed Web of Science ®Google Scholar
• Chen , Z. , Ivanov , P. C. , Hu , K. and Stanley , H. E. 2002 . Effect of nonstationarities on detrended fluctuation analysis . Physical Review E , 65 ( 4 ) : 41107 – 23 .
   Web of Science ®Google Scholar
• Du , G. and Ning , X. 2008 . Multifractal properties of Chinese stock market in Shanghai . Physica A: Statistical Mechanics and Its Applications , 387 ( 1 ) : 261 – 69 .
   Web of Science ®Google Scholar
• Duan , L. , Bahl , J. , Smith , G. J. D. , Wang , J. , Vijaykrishna , D. , Zhang , L. J. Zhang , J. X. 2008 . The development and genetic diversity of H5N1 influenza virus in China, 1996–2006 . Virology , 380 ( 2 ) : 243 – 54 .
   PubMed Web of Science ®Google Scholar
• Ducatez , M. F. , Olinger , C. M. , Owoade , A. A. , De Landtsheer , S. , Ammerlaan , W. , Niesters , H. G. M. , Osterhaus , A. D. M. E. , Fouchier , R. A. M. and Muller , C. P. 2006 . Avian flu: Multiple introductions of H5N1 in Nigeria . Nature , 442 : 37
   PubMed Web of Science ®Google Scholar
• Ducatez , M. F. , Olinger , C. M. , Owoade , A. A. , Tarnagda , Z. , Tahita , M. C. , Sow , A. De Landtsheer , S. 2007 . Molecular and antigenic evolution and geographical spread of H5N1 highly pathogenic avian influenza viruses in western Africa . Journal of General Virology , 88 ( 8 ) : 2297 – 2306 .
   PubMedGoogle Scholar
• Enserink , M. 2006 . Avian influenza. H5N1 moves into Africa, European Union, deepening global crisis . Science , 311 ( 5763 ) : 932
   PubMedGoogle Scholar
• Feder , J. 1988 . Fractals. , New York : Plenum .
   Google Scholar
• Gilbert , M. , Chaitaweesub , P. , Parakamawongsa , T. , Premashthira , S. , Tiensin , T. and Kalpravidh , W. 2006 . Free-grazing ducks and highly pathogenic avian influenza, Thailand . Emerging Infectious Diseases , 12 : 227 – 34 .
   PubMed Web of Science ®Google Scholar
• Gilbert , M. , Xiao , X. , Chaitaweesub , P. , Kalpravidh , W. , Premashthira , S. , Boles , S. and Slingenbergh , J. 2007 . Avian influenza, domestic ducks and rice agriculture in Thailand . Agriculture, Ecosystems & Environment , 119 : 409 – 15 .
   PubMed Web of Science ®Google Scholar
• Gilbert , M. , Xiao , X. , Domenech , J. , Lubroth , J. , Martin , V. and Slingenbergh , J. 2006 . Anatidae migration in the western palearctic and spread of highly pathogenic avian influenza H5N1 virus . Emerging Infectious Diseases , 12 ( 11 ) : 1650 – 56 .
   PubMed Web of Science ®Google Scholar
• Gilbert , M. , Xiao , X. , Pfeiffer , D. U. , Epprecht , M. , Boles , S. , Czarnecki , C. Chaitaweesub , P. 2008 . Mapping H5N1 highly pathogenic avian influenza risk in southeast Asia . Proceedings of the National Academy of Sciences USA , 105 ( 12 ) : 4769 – 74 .
   PubMedGoogle Scholar
• Globig , A. , Staubach , C. , Beer , M. , Köppen , U. , Fiedler , W. , Nieburg , M. Wilking , H. 2009 . Epidemiological and ornithological aspects of outbreaks of highly pathogenic avian influenza virus H5N1 of Asian lineage in wild birds in Germany, 2006 and 2007 . Transboundary and Emerging Diseases , 56 ( 3 ) : 57 – 72 .
   PubMedGoogle Scholar
• Grassberger , P. and Procaccia , I. 1983 . Characterization of strange attractors . Physical Review Letters , 50 ( 5 ) : 346 – 49 .
   Web of Science ®Google Scholar
• Guan , Y. , Peiris , J. S. M. , Lipatov , A. S. , Ellis , T. M. , Dyrting , K. C. , Krauss , S. , Zhang , L. J. , Webster , R. G. and Shortridge , K. F. 2002 . Emergence of multiple genotypes of H5N1 avian influenza viruses in Hong Kong SAR . Proceedings of the National Academy of Sciences USA , 99 ( 13 ) : 8950 – 55 .
   PubMedGoogle Scholar
• Guan , Y. , Poon , L. L. M. , Cheung , C. Y. , Ellis , T. M. , Lim , W. , Lipatov , A. S. Chan , K. H. 2004 . H5N1 influenza: A protean pandemic threat . Proceedings of the National Academy of Sciences USA , 101 ( 21 ) : 8156 – 61 .
   PubMed Web of Science ®Google Scholar
• Haggett , P. A. C. and Frey , A. E. 1977 . Local analysis in human geography , London : Edwin Arnold .
   Google Scholar
• Halsey , T. C. , Jensen , M. H. , Kadanoff , L. P. , Procaccia , I. and Shraiman , B. I. 1986 . Fractal measures and their singularities: The characterization of strange sets . Physical Review A , 33 ( 2 ) : 1141 – 51 .
   PubMed Web of Science ®Google Scholar
• Hu , K. , Ivanov , P. C. , Chen , Z. , Carpena , P. and Stanley , H. E. 2001 . Effect of trends on detrended fluctuation analysis . Physical Review E , 64 ( 1, Pt1 ) : 1 – 19 .
   Google Scholar
• Hulse-Post , D. J. , Sturm-Ramirez , K. M. , Humberd , J. , Seiler , P. , Govorkova , E. A. , Krauss , S. Scholtissek , C. 2005 . Role of domestic ducks in the propagation and biological evolution of highly pathogenic H5N1 influenza viruses in Asia . Proceedings of the National Academy of Sciences USA , 102 ( 30 ) : 10682 – 87 .
   PubMed Web of Science ®Google Scholar
• Hurst , H. 1951 . Long term storage capacity of reservoirs . Transactions of the American Society of Civil Engineers , 116
   Google Scholar
• Kantelhardt , J. W. , Rybski , D. , Zschiegner , S. A. , Braun , P. , Koscielny-Bunde , E. , Livina , V. , Havlin , S. and Bunde , A. 2003 . Multifractality of river runoff and precipitation: Comparison of fluctuation analysis and wavelet methods . Physica A: Statistical Mechanics and Its Applications , 330 ( 1–2 ) : 240 – 45 .
   Web of Science ®Google Scholar
• Kantelhardt , J. W. , Zschiegner , S. A. , Koscielny-Bunde , E. , Bunde , A. , Havlin , S. and Stanley , H. E. 2002 . Multifractal detrended fluctuation analysis of nonstationary time series . Physica A: Statistical Mechanics and Its Applications , 316 : 87
   Web of Science ®Google Scholar
• Kilpatrick , A. M. , Chmura , A. A. , Gibbons , D. W. , Fleischer , R. C. , Marra , P. P. and Daszak , P. 2006 . Predicting the global spread of H5N1 avian influenza . Proceedings of the National Academy of Sciences USA , 103 ( 51 ) : 19368 – 73 .
   PubMed Web of Science ®Google Scholar
• Krauss , S. , Obert , C. A. , Franks , J. , Walker , D. , Jones , K. , Seiler , P. Niles , L. 2007 . Influenza in migratory birds and evidence of limited intercontinental virus exchange . PLoS Pathogens , 3 ( 11 ) : e167
   Web of Science ®Google Scholar
• Lam , N. S.-N. and Lee , D. C. 1993 . Fractals in geography , Upper Saddle River, NJ : Prentice-Hall .
   Google Scholar
• Lebarbenchon , C. , Albespy , F. , Brochet , A.-L. , Grandhomme , V. , Renaud , F. , Fritz , H. Green , A. J. 2009 . Spread of avian influenza viruses by common teal (Anas crecca) in Europe . PLoS One , 4 ( 10 ) : e7289
   Web of Science ®Google Scholar
• Leung , Y. 2010 . Knowledge discovery in spatial data. , New York : Springer-Verlag .
   Google Scholar
• Li , J. , Wang , J. F. , Wu , C. Y. , Yang , Y. T. , Ji , Z. T. , Wang , H. B. , Li , X. , Fu , F. and Cui , S. J. 2006 . Spatial and temporal analysis of the effects of temperature on the spread of avian influenza . Chinese Journal of Preventive Veterinary Medicine , 28 : 408 – 11 .
   Google Scholar
• Lim , G. , Kim , S. , Lee , H. , Kim , K. and Lee , D.-I. 2007 . Multifractal detrended fluctuation analysis of derivative and spot markets . Physica A: Statistical Mechanics and Its Applications , 386 ( 1 ) : 259 – 66 .
   Google Scholar
• Liu , C.-M. , Lin , S.-H. , Chen , Y.-C. , Lin , K. C.-M. , Wu , T. -S. J. and King , C.-C. 2007 . Temperature drops and the onset of severe avian influenza and H5N1 virus outbreaks . PLoS ONE , 2 ( 2 ) : e191
   Google Scholar
• Liu , J. , Xiao , H. , Lei , F. , Zhu , Q. , Qin , K. , Zhang , X.-W. Zhang , X.-L. 2005 . Highly pathogenic H5N1 influenza virus infection in migratory birds . Science , 309 ( 5738 ) : 1206
   PubMed Web of Science ®Google Scholar
• Livina , V. , Kizner , Z. , Braun , P. , Molnar , T. , Bunde , A. and Havlin , S. 2007 . Temporal scaling comparison of real hydrological data and model runoff records . Journal of Hydrology , 336 ( 1–2 ) : 186 – 98 .
   Google Scholar
• Makowiec , D. , Galaska , R. , Dudkowska , A. , Rynkiewicz , A. and Zwierz , M. 2005 . Long-range dependencies in heart rate signals revisited . Physica A: Statistical Mechanics and Its Application , 369 ( 2 ) : 632 – 44 .
   Google Scholar
• Mandelbrot , B. 1983 . The fractal geometry of nature , New York : Freeman .
   Google Scholar
• Martinez , M. , Muoz , M. J. , Torre , A. D. L. , Iglesias , I. , Peris , S. , Infante , O. and Sanchez-Vizcaino , J. M. 2009 . Risk of introduction of H5N1 HPAI from Europe to Spain by wild water birds in autumn . Transboundary and Emerging Diseases , 56 ( 3 ) : 86 – 98 .
   PubMedGoogle Scholar
• Moone , I. , Joannis , T. M. , Fusaro , A. , Benedicitis , P. D. , Lombin , L. H. , Ularamu , H. , Egbuji , A. , Solomon , P. , Obi , T. U. , Cattoli , G. and Capua , I. 2008 . Reassortant avian influenza virus (H5N1) in poultry, Nigeria, 2007 . Emerging Infectious Diseases , 14 : 637 – 40 .
   PubMedGoogle Scholar
• Movahed , M. S. , Jafari , G. R. , Ghasemi , F. , Rahvar , S. and Tabar , M. R. R. 2006 . Multifractal detrended fluctuation analysis of sunspot time series . Journal of Statistical Mechanics: Theory and Experiment , 2006 ( 2 ) : 1 – 17 .
   Google Scholar
• Munasinghe , S. , Brown , G. , Pereira , A. , Keeble , B. , Nair , P. and Sundkvis , T. 2008 . Public health response to an avian influenza (H5N1) poultry outbreak in Suffolk, United Kingdom, in November 2007 . Eurosurveillance , 13 : 1 – 3 .
   Google Scholar
• Munster , V. J. , Baas , C. , Lexmond , P. , Waldenström , J. , Wallensten , A. , Fransson , T. Rimmelzwaan , G. F. 2007 . Spatial, temporal, and species variation in prevalence of influenza A viruses in wild migratory birds . PLoS Pathogens , 3 ( 5 ) : 636 – 38 .
   Google Scholar
• Nguyen , T. D. , Nguyen , T. V. , Vijaykrishna , D. , Webster , G. R. , Guan , Y. , Peiris , J. S. M. and Smith , G. J. D. 2008 . Multiple sublineages of influenza A virus (H5N1), Vietnam, 2005–2007 . Emerging Infectious Diseases , 13 : 632 – 36 .
   Google Scholar
• Niu , M. , Wang , F. , Liang , Q. , Yu , G. and Yu , Z. 2008 . Multifractal detrended fluctuation analysis of pressure fluctuation signals in an impinging entrained-flow gasifier . Chemical Engineering Journal , 136 ( 2–3 ) : 364 – 72 .
   Google Scholar
• Normile , D. 2005a . Are wild birds to blame? . Science , 310 : 426 – 28 .
   PubMed Web of Science ®Google Scholar
• Normile , D. 2005b . Avian influenza: Europe scrambles to control deadly H5N1 strain . Science , 310 ( 5747 ) : 417
   PubMedGoogle Scholar
• Normile , D. 2006a . Avian influenza: Evidence points to migratory birds in H5N1 spread . Science , 311 : 1225
   PubMed Web of Science ®Google Scholar
• Normile , D. 2006b . Avian influenza: Wild birds only partly to blame in spreading H5N1 . Science , 312 : 1415
   Google Scholar
• Olsen , B. , Munster , V. J. , Wallensten , A. , Waldenström , J. , Osterhaus , A. D. M. E. and Fouchier , R. A. M. 2006 . Global patterns of influenza A virus in wild birds . Science , 312 ( 5772 ) : 384 – 88 .
   PubMed Web of Science ®Google Scholar
• Ozawa , Y. , Makino , S. , Park , J. , Chang , J. , Kim , J. and An , S. 2006 . A review of recent unexpected animal disease events in Japan and Korea and the follow-up action taken . Revue Scientifique et Technique International Office of Epizootics , 25 : 125 – 35 .
   PubMedGoogle Scholar
• Peng , C. K. , Buldyrev , S. V. , Havlin , S. , Simons , M. , Stanley , H. E. and Goldberger , A. L. 1994 . Mosaic organization of DNA nucleotides . Physical Review E , 49 ( 2 ) : 1685 – 89 .
   PubMed Web of Science ®Google Scholar
• Preiser , K. H. 2006 . Influenza report 2006 , Paris, Cagliari, Wuppertal, Sevilla: Flying Publish .
   Google Scholar
• Salzberg , S. L. , Kingsford , C. , Cattoli , G. , Spiro , D. J. , Janies , D. A. , Aly , M. M. Brown , I. H. 2007 . Genome analysis linking recent European and African influenza (H5N1) viruses . Emerging Infectious Diseases , 13 ( 5 ) : 713 – 18 .
   PubMedGoogle Scholar
• Shang , P. , Lu , Y. and Kamae , S. 2008 . Detecting long-range correlations of traffic time series with multifractal detrended fluctuation analysis . Chaos, Solitons & Fractals , 36 ( 1 ) : 82 – 90 .
   Web of Science ®Google Scholar
• Si , Y. , Skidmore , A. K. , Wang , T. , de Boer , W. F. , Debba , P. , Toxopeus , A. G. , Li , L. and Prins , H. H. 2009 . Spatio-temporal dynamics of global H5N1 outbreaks match bird migration patterns . Geospatial Health , 4 : 65 – 78 .
   PubMed Web of Science ®Google Scholar
• Smallman-Raynor , M. and Cliff , A. D. 2008 . The geographical spread of avian influenza a (H5N1): Panzootic transmission (December 2003–May 2006), pandemic potential, and implications . Annals of the Association of American Geographers , 98 : 553 – 82 .
   Web of Science ®Google Scholar
• Smith , G. J. D. , Fan , X. H. , Wang , J. , Li , K. S. , Qin , K. , Zhang , J. X. Vijaykrishna , D. 2006 . Emergence and predominance of an H5N1 influenza variant in China . Proceedings of the National Academy of Sciences USA , 103 ( 45 ) : 16936 – 41 .
   PubMedGoogle Scholar
• Smith , G. J. D. , Naipospos , T. S. P. , Nguyen , T. D. , de Jong , M. D. , Vijaykrishna , D. , Usman , T. B. Hassan , S. S. 2006 . Evolution and adaptation of H5N1 influenza virus in avian and human hosts in Indonesia and Vietnam . Virology , 350 ( 2 ) : 258 – 68 .
   PubMedGoogle Scholar
• Szeleczky , Z. , Dán , A. , Ursu , K. , Ivanics , E. , Kiss , I. , Erdélyi , K. , Bel , S. , Muller , C. P. , Brown , I. H. and Bálint , A. 2009 . Four different sublineages of highly pathogenic avian influenza H5N1 introduced in Hungary in 2006–2007 . Veterinary Microbiology , 139 ( 1–2 ) : 24 – 33 .
   PubMedGoogle Scholar
• Telesca , L. , Lapenna , V. and Macchiato , M. 2005 . Multifractal fluctuations in earthquake-related geoelectrical signals . New Journal of Physics , 7 : 214
   Google Scholar
• U.S. Geological Survey . 2010 . Migratory bird flyways: Potential pathways for distribution of avian influenza . http://alaska.usgs.gov/science/biology/avianinfluenza/flyways.html (last accessed 22 March 2010)
   Google Scholar
• Wallace , R. G. , Hodac , H. , Lathrop , R. H. and Fitch , W. M. 2007 . A statistical phylogeography of influenza A H5N1 . Proceedings of the National Academy of Sciences USA , 104 ( 11 ) : 4473 – 78 .
   PubMed Web of Science ®Google Scholar
• Wang , G. , Zhan , D. , Li , L. , Lei , F. , Liu , B. , Liu , D. Xiao , H. 2008 . H5N1 avian influenza re-emergence of Lake Qinghai: Phylogenetic and antigenic analyses of the newly isolated viruses and roles of migratory birds in virus circulation . Journal of General Virology , 89 ( 3 ) : 697 – 702 .
   PubMedGoogle Scholar
• Webster , R. G. , Bean , W. J. , Gorman , O. T. , Chambers , T. M. and Kawaoka , Y. 1992 . Evolution and ecology of influenza A viruses . Microbiology Review , 56 ( 1 ) : 152 – 79 .
   PubMedGoogle Scholar
• Webster , R. G. , Peiris , M. , Chen , H. and Guan , Y. 2006 . H5N1 outbreaks and enzootic influenza . Emerging Infectious Diseases , 12 ( 1 ) : 3 – 8 .
   PubMedGoogle Scholar
• World Health Organization (WHO) . 2006 . Avian influenza (“bird flu”) . http://www.who.int/mediacentre/factsheets/avianinfluenza/en/ (last accessed 22 March 2010)
   Google Scholar
• World Health Organization (WHO) . 2010a . Cumulative number of confirmed human cases of avian influenza a/(H5N1) . http://www.who.int/csr/disease/avianinfluenza/country/casestable20100316/en/index.html (last accessed 22 March 2010)
   Google Scholar
• World Health Organization (WHO) . 2010b . H5N1 avian influenza: Timeline of major events, 04 January 2010 . http://www.who.int/csr/disease/avianinfluenza/timeline100104.pdf (last accessed 14 May 2010).
   Google Scholar
• World Organisation for Animal Health (OIE) . 2010 . Update on highly pathogenic avian influenza in animals . http://www.oie.int/downld/avian%20influenza/aai-asia.htm (last accessed 10 March 2010)
   Google Scholar
• Xu , X. , Subbarao , K. , Cox , N. J. and Guo , Y. 1999 . Genetic characterization of the pathogenic influenza A/goose/guangdong/1/96 (H5N1) virus: Similarity of its hemagglutinin gene to those of H5N1 viruses from the 1997 outbreaks in Hong Kong . Virology , 261 ( 1 ) : 15 – 19 .
   PubMed Web of Science ®Google Scholar
• Yee , K. S. , Carpenter , T. E. and Cardona , C. J. 2009 . Epidemiology of H5N1 avian influenza: Comparative immunology . Microbiology and Infectious Diseases , 32 ( 4 ) : 325 – 40 .
   PubMedGoogle Scholar
• Yu , Z.-G. , Anh , V. and Eastes , R. 2009 . Multifractal analysis of geomagnetic storm and solar flare indices and their class dependence . Journal of Geophysical Research , 114 ( A5 ) : A05214
   Google Scholar
• Yu , Z. G. , Leung , Y. , Chen , Y. Q. , Zhang , Q. and Anh , V. 2009 . Multifractal analysis of daily rainfall in the Pearl River basin of China . Unpublished paper
   Google Scholar