An investigation into the statistical properties of TB episodes in a South African community with high HIV prevalence

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dc.contributor.authorPretorius C.
dc.contributor.authorDodd P.
dc.contributor.authorWood R.
dc.date.accessioned2011-05-15T15:59:49Z
dc.date.available2011-05-15T15:59:49Z
dc.date.issued2011
dc.description.abstractContinuous differential equations are often applied to small populations with little time spent on understanding uncertainty brought about by small-population effects. Despite large numbers of individuals being latently infected with Mycobacterium tuberculosis (TB), progression from latent infection to observable disease is a relatively rare event. For small communities, this means case counts are subject to stochasticity, and deterministic models may not be appropriate tools for interpreting transmission trends. Furthermore, the nonlinear nature of the underlying dynamics means that fluctuations are autocorrelated, which can invalidate standard statistical analyses which assume independent fluctuations.Here we extend recent work using a system of differential equations to study the HIV-TB epidemic in Masiphumelele, a community near Cape Town in South Africa [Bacaër, et al., J. Mol. Biol. 57(4), 557-593] by studying the statistical properties of active TB events. We apply van Kampen's system-size (or population-size) expansion technique to obtain an approximation to a master equation describing the dynamics. We use the resulting Fokker-Planck equation and point-process theory to derive two-time correlation functions for active TB events. This method can be used to gain insight into the temporal aspect of cluster identification, which currently relies on DNA classification only. © 2010.
dc.description.versionArticle
dc.identifier.citationJournal of Theoretical Biology
dc.identifier.citation270
dc.identifier.citation1
dc.identifier.issn225193
dc.identifier.other10.1016/j.jtbi.2010.10.012
dc.identifier.urihttp://hdl.handle.net/10019.1/11382
dc.subjectdisease prevalence
dc.subjectdisease transmission
dc.subjectepidemic
dc.subjecthuman immunodeficiency virus
dc.subjectstatistical analysis
dc.subjecttuberculosis
dc.subjectarticle
dc.subjectbiostatistics
dc.subjectepidemic
dc.subjectHuman immunodeficiency virus infection
dc.subjectHuman immunodeficiency virus prevalence
dc.subjectmathematical model
dc.subjectmortality
dc.subjectpopulation size
dc.subjectpriority journal
dc.subjectSouth Africa
dc.subjecttuberculosis
dc.subjectSouth Africa
dc.subjectMycobacterium tuberculosis
dc.titleAn investigation into the statistical properties of TB episodes in a South African community with high HIV prevalence
dc.typeArticle
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