{"refrec":{"BRefID":231125,"RR":"<b>Wang, R.H.; Jin, Z.; Liu, Q.X.; van de Koppel, J.; Alonso, D.</b> (2012). A Simple Stochastic Model with Environmental Transmission Explains Multi-Year Periodicity in Outbreaks of Avian Flu. <i>PLoS One 7(2)</i>: e28873. <a href=\"http://dx.doi.org/10.1371/journal.pone.0028873\" target=\"_blank\">dx.doi.org/10.1371/journal.pone.0028873</a>","BEntID":222837,"PublicFlag":1,"CheckedFlag":1,"wosflag":1,"vabbflag":1,"RefStringPartII":". <i>PLoS One 7(2)</i>: e28873. <a href=\"https://dx.doi.org/10.1371/journal.pone.0028873\" target=\"_blank\">https://dx.doi.org/10.1371/journal.pone.0028873</a>","DocTypID":8,"DocType":"Journal article","MarineFlag":0,"FreshFlag":0,"BrackishFlag":0,"TerrestrialFlag":0,"Authorstring":"Wang, R.H.; Jin, Z.; Liu, Q.X.; van de Koppel, J.; Alonso, D.","OrigTitleTranslFlag":0,"Authorstringtrunc":"Wang, R.H. <i>et al.</i>","Englishabstract":"Avian influenza virus reveals persistent and recurrent outbreaks in North American wild waterfowl, and exhibits major outbreaks at 2-8 years intervals in duck populations. The standard susceptible-infected-recovered (SIR) framework, which includes seasonal migration and reproduction, but lacks environmental transmission, is unable to reproduce the multi-periodic patterns of avian influenza epidemics. In this paper, we argue that a fully stochastic theory based on environmental transmission provides a simple, plausible explanation for the phenomenon of multi-year periodic outbreaks of avian flu. Our theory predicts complex fluctuations with a dominant period of 2 to 8 years which essentially depends on the intensity of environmental transmission. A wavelet analysis of the observed data supports this prediction. Furthermore, using master equations and van Kampen system-size expansion techniques, we provide an analytical expression for the spectrum of stochastic fluctuations, revealing how the outbreak period varies with the environmental transmission.","AbstractOtherLang":null,"BibLvlCode":"AS","StandardTitle":"A Simple Stochastic Model with Environmental Transmission Explains Multi-Year Periodicity in Outbreaks of Avian Flu","OrigTitleLangCode":"en","OrigTitleLangCodeExtended":"eng","OrigTitleLangID":15,"DateLastModified":{"date":"2024-12-10 01:33:01.897972","timezone_type":1,"timezone":"+01:00"},"UserAccessRight":null,"UserAccID":null,"AuthorKeywords":null,"OtherDescriptors":null,"Notes":null,"AnaPub":2012,"MonPub":null,"DateUpdate":"2014-08-29","DateCreate":"2013-12-01","SecASFANote":null,"ConfID":null,"PeerRev":1,"VlizCoreFlag":1,"WoScode":"WOS:000302853600002","VABBcode":null,"OpenAcc":1,"DOI":"10.1371/journal.pone.0028873"},"refs":null,"anarec":{"AnaID":231125,"PubliDate":2012,"Pagination":"e28873","XtraPublOfAnaID":null,"ISBN":null,"Volume":"7","Issue":"2","BRefMon":null,"BRefMonRR":null,"BRefXtra":null,"BRefXtraRR":null,"SerBRefID":123954,"SerRR":"PLoS One. 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