title: The Dynamics of Ascaris lumbricoides Infections.
abstract: 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.
authors.affiliation: MACSI, University of Limerick, Limerick, Ireland. andrew.fowler@ul.ie.|OCIAM, University of Oxford, Oxford, UK. andrew.fowler@ul.ie.
authors.forename: A C
authors.initials: AC
authors.lastname: Fowler
authors.affiliation: Mathematics Institute, University of Warwick, Coventry, UK.|Liverpool School of Tropical Medicine, Liverpool, UK.
authors.forename: T Déirdre
authors.initials: TD
authors.lastname: Hollingsworth
mesh_terms: D000818:Animals; D001196:Ascariasis / Q000188:drug therapy / Q000469:parasitology* / Q000635:transmission; D017164:Ascaris lumbricoides; D016010:Binomial Distribution; D004064:Digestive System / Q000469:parasitology; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D017711:Nonlinear Dynamics; D010270:Parasite Egg Count; D013269:Stochastic Processes
keywords: Ascaris lumbricoides; Infectious diseases; Mathematical model; Negative binomial distribution