The correlation structure of epidemic models
type: Item
instance of: scholarly article
title: The correlation structure of epidemic models
zbMATH Open document ID: 0799.92018
DOI: 10.1016/0025-5564(93)90017-5
author: Peter Donnelly
published in: Mathematical Biosciences
publication date: 1994-11-17T00:00:00Z
review text: For a general Markov SIS epidemic model, the author proves positive correlation between the fates of individuals at different times. For the same model with two diseases, ``positive interference'' between diseases results in positive correlations between individuals w.r.t. either disease, and ``competition'' between diseases results in negative correlation between diseases and positive correlation within each disease. These results are generalized to several diseases if they can be grouped into two classes such that there is positive interference within each class and competition between classes. The results use coupling arguments and adequate partial orderings of the state spaces and are based on a theorem connecting monotonicity of Markov processes on finite partially ordered sets and positive correlations due to \textit{T. E. Harris} [Ann. Probab. 5, 451-454 (1977; Zbl 0381.60072)]. The same technique is used to obtain positive correlation between the fates of individuals at different times for a general Markov SIR epidemic model if one does not distinguish between infected and removed states (for otherwise no appropriate partial ordering is available).
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 60J20
Mathematics Subject Classification ID: 60J99
zbMATH DE Number: 501033
zbMATH Keywords: positive interference
zbMATH Keywords: competition
zbMATH Keywords: general Markov SIS epidemic model
zbMATH Keywords: positive correlation
zbMATH Keywords: negative correlation
zbMATH Keywords: coupling arguments
zbMATH Keywords: partial orderings
zbMATH Keywords: monotonicity of Markov processes
zbMATH Keywords: finite partially ordered sets
zbMATH Keywords: general Markov SIR epidemic model
reviewed by: Carlos A. dos Santos Braumann
MaRDI profile type: Publication
full work available at URL: 0025-5564(93)90017-5
OpenAlex ID: W2025965616
Wikidata QID: Q52390943
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description: scientific article; zbMATH DE number 501033