The Dynamics of Ascaris lumbricoides Infections

Abstract

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 pre-disposition to the infection. Powered by Editorial Manager® and ProduXion Manager® from Aries Systems CorporationThe dynamics of Ascaris lumbricoides infections AbstractThe 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 pre-disposition to the infection. AbstractThe 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 ...

Seasonally timed treatment programs for Ascaris lumbricoides to increase impact—An investigation using mathematical models

“…This is a new model framework inspired by the well-established two-stage delay differential equation model developed by Anderson and May that considers the interaction between the mean worm burden ( M ) and the number of infective larval stages present in the immediate environment ( L ) [ 34 ]. Using a similar approach to Fowler et al [ 35 ], this new framework is easier to describe, implement and fit as it removes the need for delays. Here we additionally consider the mean number of juvenile worms per host ( J ) and the total count of immature eggs in the environment ( E ).…”

Evaluating the Evidence for Lymphatic Filariasis Elimination

“…The probability of elimination, given a particular prevalence (e.g., 1%), can be calculated by considering the probability that a chain of transmission will die out (in mathematics we call this chain a branching process [ 22 ] ). These types of branching process methods have been used for soil-transmitted helminths [ 23 , 24 ], but have been adapted here to account for vector-borne transmission with an aggregated bite risk [ 25 , 26 ].…”

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“…We set a uniform prior for log of the mean number of worms log( W ) ∼ U [log(0.01), log(60)] and a uniform prior for the degree of clumping k ∼ U [0, 3]. Although typical values for mean worm burden are 10-20 (33), much higher numbers have been observed in field conditions (19; 34).…”