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


Pretorius, C; Dodd, P; Wood, R; (2011) An investigation into the statistical properties of TB episodes in a South African community with high HIV prevalence. Journal of theoretical biology, 270 (1). pp. 154-163. ISSN 0022-5193 DOI: https://doi.org/10.1016/j.jtbi.2010.10.012

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Abstract

Continuous 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 [Bacaer, 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. (C) 2010 Published by Elsevier Ltd.

Item Type: Article
Keywords: Dynamical model, Master equation, Point process, Two-time correlation, function, HUMAN-IMMUNODEFICIENCY-VIRUS, TUBERCULOSIS-CONTROL, MYCOBACTERIUM-TUBERCULOSIS, UNDIAGNOSED TUBERCULOSIS, MOLECULAR, EPIDEMIOLOGY, DRUG-USERS, INFECTION, IMPACT, TRANSMISSION, STRATEGIES
Faculty and Department: Faculty of Epidemiology and Population Health > Dept of Infectious Disease Epidemiology
Research Centre: TB Centre
PubMed ID: 21056044
Web of Science ID: 286406700018
URI: http://researchonline.lshtm.ac.uk/id/eprint/1116

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