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A basic model for the transmission dynamics of filarial infections
To provide a comprehensible modeling framework, the transmission cycle
of a filarial infection is described deterministically,
neglecting the age structure of the human population.
Parameter values are adapted to West African savannah onchocerciasis,
for which regulatory processes are better investigated.
For terms used in the following, see
Glossary.
The changes in the burdens of adult female parasites, w,
and microfilariae, m, with time t are given by Equation I and Equation II:
where ATP=annual transmission potential;
=parasite establishment rate
(PER; i.e. number of adult female parasites establishing per host per year);
1/w=ten years: life expectancy of adult female parasites;
1/h=50 years: life expectancy of humans,
=mating probability, for promiscuous parasites given by
(w)=1-(1+w/k)-(k+1),
whereby the sum of male and female worms is assumed to be geometrically distributed,
hence k»1;
=rate at which microfilariae (Mf) per mg skin snip result
from the number of adult female O. volvulus per year.
1/m=1 year: life expectancy of Mf.
The coexistence of immunosuppression and protective immunity
in human hosts is assumed to operate on the PER, implemented as
Where 0=1 per year: number of adult female parasites
establishing in a noninfected host per year;
fF(w)=(1+csw)/(1+sw): Facilitated parasite establishment
due to parasite-induced immunosuppression with parameters
0*c=5.75 per year: number of adult female parasites
establishing in a heavily infected host per year;
s=0.1: slope by which 0*c is achieved;
f L(ATP)=( ATP)/(1+ ATP):
Limited parasite establishment due to protective immunity
against infectious larvae (L3) with parameter =0.06.
Limitation for Mf is implemented as (Equation IV)
b=5 Mf per mg skin snip are contributed per adult female worm
in hosts with low parasite burdens; k = 0.034:
slope by which the asymptote b m/k=147 Mf per skin snip is achieved.
Survival of flies with respect to the time-dependent processes
is assumed to be negligibly small so that it does not need
to be implemented dynamically. Limitation in the number of L3
developing from Mf ingested during a blood meal is given by Equation V:
with a1=0.021 and a2=0.0088.
According to precontrol data from the Onchocerciasis Control Programme,
the ATP increases linearly with the annual biting rate (ABR) at
slope =0.02, thus
Using this model, sensitivity analyses on the eradicability of
onchocerciasis have been investigated in Duerr et al. 2005.
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Related pages:
Eradicability overview,
Eradicability of onchocerciasis.
Further reading:
Duerr HP, Dietz K, Eichner M, 2005.
Determinants of the eradicability of filarial infections: a conceptual approach.
Trends in Parasitology 21: 88-96.
Abstract at PubMed
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Responsible for this page:
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Dr. H.-P. Duerr
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Webmaster:
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Prof. Dr. M. Eichner
(last change of this page on
13 July 2009)
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Cooperation with:
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Prof. K. Dietz, Institut für Medizinische Biometrie (IMB), Tübingen
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Dr. M. Eichner
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Financial support by:
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Deutsche Forschungsgemeinschaft (DFG, DI 308/12-1)
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Disclaimer:
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Eberhard-Karls-University Tübingen,
Tübingen University Hospital,
the Department for Medical Biometry (IMB),
and the authors of this page disclaim all liability for the content of any page referenced by hyper-link from this page
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