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On the variance mean ratio in models of parasite distributions

Part of: Markov processes

Published online by Cambridge University Press:  19 February 2016

Andrew D. Barbour  and
Andrea Pugliese
Andrew D. Barbour*
Affiliation:
Universität Zürich
Andrea Pugliese*
Affiliation:
Università di Trento
*
∗ Postal address: Abteilung Angewandte Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland. Email address: [email protected]
∗∗ Postal address: Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38050 Povo (TN), Italy. Email address: [email protected]
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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.

Keywords

Quasi-stationary distributionsmodels of parasitic infectionsover-dispersed distributionsvariance-to-mean ratio

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces 92D30: Epidemiology
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 3 , September 2000 , pp. 701 - 719
Copyright
Copyright © Applied Probability Trust 2000 

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