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A stochastic model for the transmission of bilharzia


Barbour, A D (1978). A stochastic model for the transmission of bilharzia. Mathematical Biosciences, 38(3-4):303-312.

Abstract

Although the transmission mechanisms of helminthic infections are extremely complicated, models based on unrealistically simplified assumptions may still be useful as a guide to controlling the diseases. The basic model discussed in this paper is a stochastic version of Macdonald's model. It is used to give an estimate of the probability that an infected person entering a community previously free of the disease will cause it to become established there. A more complicated model is then put forward, which takes rather more of the detail of the transmission cycle into account. This in principle enables a more realistic estimate to be obtained, and it is shown that, under reasonable hypotheses, the estimate is very similar to that suggested by the basic model. Since the true probability depends heavily on the fine detail of the transmission mechanisms, however, the importance of such estimates is largely confined to their qualitative response to changes in the underlying parameters.

Although the transmission mechanisms of helminthic infections are extremely complicated, models based on unrealistically simplified assumptions may still be useful as a guide to controlling the diseases. The basic model discussed in this paper is a stochastic version of Macdonald's model. It is used to give an estimate of the probability that an infected person entering a community previously free of the disease will cause it to become established there. A more complicated model is then put forward, which takes rather more of the detail of the transmission cycle into account. This in principle enables a more realistic estimate to be obtained, and it is shown that, under reasonable hypotheses, the estimate is very similar to that suggested by the basic model. Since the true probability depends heavily on the fine detail of the transmission mechanisms, however, the importance of such estimates is largely confined to their qualitative response to changes in the underlying parameters.

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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:1978
Deposited On:04 Nov 2009 07:57
Last Modified:05 Apr 2016 13:30
Publisher:Elsevier
ISSN:0025-5564
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/0025-5564(78)90051-2
Related URLs:http://user.math.uzh.ch/barbour/pub/Barbour/StochasticBilharzia.pdf (Author)

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