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Stochastic models of a parasitic infection, exhibiting three basic reproduction ratios


Luchsinger, C J (2001). Stochastic models of a parasitic infection, exhibiting three basic reproduction ratios. Journal of Mathematical Biology, 42(6):532-554.

Abstract

Two closely related stochastic models of parasitic infection are investigated: a non-linear model, where density dependent constraints are included, and a linear model appropriate to the initial behaviour of an epidemic. Host-mortality is included in both models. These models are appropriate to transmission between homogeneously mixing hosts, where the amount of infection which is transferred from one host to another at a single contact depends on the number of parasites in the infecting host. In both models, the basic reproduction ratio R 0 can be defined to be the lifetime expected number of offspring of an adult parasite under ideal conditions, but it does not necessarily contain the information needed to separate growth from extinction of infection. In fact we find three regions for a certain parameter where different combinations of parameters determine the behavior of the models. The proofs involve martingale and coupling methods.

Abstract

Two closely related stochastic models of parasitic infection are investigated: a non-linear model, where density dependent constraints are included, and a linear model appropriate to the initial behaviour of an epidemic. Host-mortality is included in both models. These models are appropriate to transmission between homogeneously mixing hosts, where the amount of infection which is transferred from one host to another at a single contact depends on the number of parasites in the infecting host. In both models, the basic reproduction ratio R 0 can be defined to be the lifetime expected number of offspring of an adult parasite under ideal conditions, but it does not necessarily contain the information needed to separate growth from extinction of infection. In fact we find three regions for a certain parameter where different combinations of parameters determine the behavior of the models. The proofs involve martingale and coupling methods.

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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
Language:English
Date:June 2001
Deposited On:23 Apr 2009 06:47
Last Modified:06 Dec 2017 19:33
Publisher:Springer
ISSN:0303-6812
Publisher DOI:https://doi.org/10.1007/s002850100082
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1845591

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