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The Anderson-May model of human parasite infections and specifically that for the intestinal worm Ascaris lumbricoides is reconsidered, with a view to deriving the observed characteristic negative binomial distribution which is frequently found in human communities. The means to obtaining this result lies in reformulating the continuous Anderson-May model as a stochastic process involving two essential populations, the density of mature worms in the gut, and the density of mature eggs in the environment. The resulting partial differential equation for the generating function of the joint probability distribution of eggs and worms can be partially solved in the appropriate limit where the worm lifetime is much greater than that of the mature eggs in the environment. Allowing for a mean field nonlinearity, and for egg immigration from neighbouring communities, a negative binomial worm distribution can be predicted, whose parameters are determined by those in the continuous Anderson-May model; this result assumes no variability in predisposition to the infection.

Original publication

DOI

10.1007/s11538-016-0164-2

Type

Journal article

Journal

Bulletin of mathematical biology

Publication Date

11/04/2016

Volume

78

Pages

815 - 833

Addresses

MACSI, University of Limerick, Limerick, Ireland. andrew.fowler@ul.ie.

Keywords

Digestive System, Animals, Humans, Ascaris lumbricoides, Ascariasis, Parasite Egg Count, Binomial Distribution, Stochastic Processes, Nonlinear Dynamics, Models, Biological, Mathematical Concepts