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On the variance-to-mean ratio in models of parasite distributions


Barbour, A D; Pugliese, A (2000). On the variance-to-mean ratio in models of parasite distributions. Advances in Applied Probability, 32(3):701-719.

Abstract

We study the variance-to-mean ratio of the distributions of parasites among hosts for some models of parasite infection, using the cohort approach. We consider a model with density dependence in parasite mortality, and two different formulations of disease induced host mortality. We show that the distributions of parasites, conditional on host survival, converge to quasi-stationary distributions as host age increases. When there is density dependence in parasite mortality, the limiting variance-to-mean ratio is less than 1 (an `under-dispersed' distribution). In contrast, the two modes of disease induced host mortality show that either over- or underdispersed distributions may result.

We study the variance-to-mean ratio of the distributions of parasites among hosts for some models of parasite infection, using the cohort approach. We consider a model with density dependence in parasite mortality, and two different formulations of disease induced host mortality. We show that the distributions of parasites, conditional on host survival, converge to quasi-stationary distributions as host age increases. When there is density dependence in parasite mortality, the limiting variance-to-mean ratio is less than 1 (an `under-dispersed' distribution). In contrast, the two modes of disease induced host mortality show that either over- or underdispersed distributions may result.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Quasi-stationary distributions; models of parasitic infections; over-dispersed distributions; variance-to-mean ratio
Language:English
Date:2000
Deposited On:04 Mar 2010 14:16
Last Modified:05 Apr 2016 13:25
Publisher:Applied Probability Trust
ISSN:0001-8678
Publisher DOI:10.1239/aap/1013540240
Related URLs:http://www.jstor.org/stable/1428409
Permanent URL: http://doi.org/10.5167/uzh-22066

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