Richards model revisited : validation by and application to infection dynamics

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dc.contributor.authorXiang-Sheng Wang
dc.contributor.authorJianhong Wu
dc.contributor.authorYong Yang
dc.date.accessioned2013-08-08T16:58:47Z
dc.date.available2013-08-08T16:58:47Z
dc.date.copyright2012
dc.date.issued2012
dc.description.abstractEver since Richards proposed his flexible growth function more than half a century ago, it has been a mystery that this empirical function has made many incredible coincidences with real ecological or epidemic data even though one of its parameters (i.e., the exponential term) does not seem to have clear biological meaning. It is therefore a natural challenge to mathematical biologists to provide an explanation of the interesting coincidences and a biological interpretation of the parameter. Here we start from a simple epidemic SIR model to revisit Richards model via an intrinsic relation between both models. Especially, we prove that the exponential term in the Richards model has a one-to-one nonlinear correspondence to the basic reproduction number of the SIR model. This one-to-one relation provides us an explicit formula in calculating the basic reproduction number. Another biological significance of our study is the observation that the peak time is approximately just a serial interval after the turning point. Moreover, we provide an explicit relation between final outbreak size, basic reproduction number and the peak epidemic size which means that we can predict the final outbreak size shortly after the peak time. Finally, we introduce a constraint in Richards model to address over fitting problem observed in the existing studies and then apply our method with constraint to conduct some validation analysis using the data of recent outbreaks of prototype infectious diseases such as Canada 2009 H1N1 outbreak, GTA 2003 SARS outbreak, Singapore 2005 dengue outbreak, and Taiwan 2003 SARS outbreak. Our new formula gives much more stable and precise estimate of model parameters and key epidemic characteristics such as the final outbreak size, the basic reproduction number, and the turning point, compared with earlier simulations without constraints.en
dc.formatTexten
dc.format.extent1 digital file (p. 12-19)en
dc.format.mimetypeApplication/pdf
dc.identifier.citationXiang-Sheng Wang, Jianhong Wu, & Yong Yang (2012). Richards model revisited: Validation by and application to infection dynamics. Journal of Theoretical Biology, 313, 12-19.doi.org/10.1016/j.jtbi.2012.07.024en
dc.identifier.issn0022-5193
dc.identifier.urihttp://hdl.handle.net/10625/51481
dc.language.isoen
dc.publisherElsevieren
dc.subjectRICHARDS MODELen
dc.subjectSIR MODELen
dc.subjectASYMPTOTIC APPROXIMATIONen
dc.subjectBASIC REPRODUCTION NUMBERen
dc.subjectOVERFITTINGen
dc.subjectMATHEMATICAL MODELSen
dc.subjectPOPULATION GROWTHen
dc.subjectBIOLOGYen
dc.titleRichards model revisited : validation by and application to infection dynamicsen
dc.typeJournal Article (peer-reviewed)en
idrc.copyright.holderElsevier Ltd.
idrc.dspace.accessIDRC Onlyen
idrc.noaccessDue to copyright restrictions the full text of this research output is not available in the IDRC Digital Library or by request from the IDRC Library. / Compte tenu des restrictions relatives au droit d'auteur, le texte intégral de cet extrant de recherche n'est pas accessible dans la Bibliothèque numérique du CRDI, et il n'est pas possible d'en faire la demande à la Bibliothéque du CRDI.en
idrc.project.componentnumber104519010
idrc.project.number104519
idrc.project.titleInternational Research Chairs Initiative (IRCI)en
idrc.recordsserver.bcsnumberIC01-3412-148
idrc.rims.adhocgroupIDRC SUPPORTEDen

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IDRC Research Results / Résultats de recherches du CRDI
2010-2019 / Années 2010-2019
Modelling and controlling infectious diseases / Se servir de la modélisation pour lutter contre les maladies infectieuses