Compound processes as models for clumped parasite data

Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland.
Mathematical biosciences (Impact Factor: 1.3). 09/2009; 222(1):27-35. DOI: 10.1016/j.mbs.2009.08.007
Source: PubMed


Compound processes are proposed as models for the acquisition of hydatid cysts in sheep, caused by the parasite Echinococcus granulosus. The hypothesis of a clumped infection process against single ingestions is tested and it is shown that the clump-based approach provides a more accurate description of the two data sets investigated. Models with simple and mixed Poisson incidence processes and different clump size distributions are compared. A mixed Poisson incidence process with a zero-truncated negative binomial distribution for the clump sizes is shown to give an adequate description, suggesting that the acquisition of hydatid cysts in the sheep population is heterogeneous, and that the clump sizes are aggregated. The estimates of the parameters derived from the data take plausible values. The average infection rate and the clump size distribution are comparable in both data sets. Goodness-of-fit measures indicate that the model fits the data reasonably well.

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    • "[13], it is shown that a compound mixed Poisson process with a zero-truncated negative binomial distribution for the number of established cysts per ingested clump of infective material provides an adequate fit for the age-dependent cyst distribution in sheep. The model indicates that the rate of ingestion of clumps is heterogeneous within the sheep population, and that the clump sizes are aggregated. "
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    ABSTRACT: A mechanistic individual-based model for the infection dynamics of the parasite Echinococcus granulosus in a two-host transmission system is proposed. The model describes the individual densities of the parasites in the two host populations. The architecture consists of two sub-processes for the acquisition and severity of infection in the host populations and a superimposed infection contact scheme between the hosts. The parasite dynamics within the host population are modeled using a compound mixed Poisson process for the sheep and a shot-noise process for the dogs. All model parameters are estimated based on available data. The fitted model is then used for simulations of the transmission dynamics between the two hosts to investigate environmental factors and evaluate intervention programs.
    Full-text · Article · Jul 2013 · International Journal of Biomathematics
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    • "Such models have demonstrated that the mode of acquisition may have a considerable impact on STH population biology, not least because it could explain some of the over-dispersion (relative to the Poisson distribution) of the number of worms per host (Grenfell et al., 1995; Isham, 1995; Pugliese et al., 1998; Tallis and Leyton, 1969), a characteristic feature of STH populations (Anderson and May, 1992). Despite this, there have been very few attempts at analysing data with the purpose of discerning the predominant mode by which hosts acquire infective stages from the environment (Heinzmann et al., 2009). The size of a worm within the human gut will depend on its size at establishment, the time since establishment (for Ascaris lumbricoides , we define the worm's age to be this period plus an approximately 2 week migratory phase (Crompton, 1989)) and on the relationship between size and age (determined by the growth rate). "
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    ABSTRACT: Shot noise processes are introduced to model aggregated parasitic count data arising from clumped superinfections coupled with different decay mechanisms of the ingested parasite clumps. The corresponding likelihood functions are derived by using Laplace transforms. The models are fitted to samples with Echinococcus granulosus parasites in dogs from Kazakhstan, Tunisia and China. It is shown that parameter estimates take plausible values and that the decay dynamics is comparable in the three samples. The results indicate that dogs cease to be infectious after about 8 months, and that infections of dogs occur at a low rate, but the ingested parasite load per clump is in the thousands.
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