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Persistence graphs
Persistence graphs show equilibrium parasite densities,
dependent on the number of vectorhost contacts [annual biting rate,
ABR).
The red curve shows the stable, positive equilibria:
provided that there are sufficient vectorhost contacts and parasites,
the average parasite density in human hosts is represented by this curve.
The green line shows the stable, trivial equilibria (parasite density = 0):
transmission of the infection is not possible because of
too few vectorhost contacts or too few parasites.
The blue-dashed curve, resulting from
breakpoint-inducing facilitation processes,
represents the unstable equilibria (breakpoints):
if the parasite density falls short of a breakpoint,
the system will tend towards the trivial equilibrium and the infection
will become extinct without further efforts
(successful intervention, C1).
If the parasite density exceeds a breakpoint,
the system will return to the stable,
positive equilibrium and the infection will continue to persist
(untimely cancelled intervention, C2).
The vertical arrows represent
the dynamic behavior of the system: starting from any point on a line,
an arrow points to the equilibrium parasite density at which
the undisturbed system will stabilize.
In the green section of the graph,
the infection cannot persist because the critical transmission threshold
(TBR, point A)
is not reached.
In the blue section of the graph, the infection can be eliminated
by reducing the parasite density below the ABR-specific breakpoint.
Point B indicates an ABR at which facilitation-induced breakpoints
disappear so that the stable zero equilibria (green line) exist only
because of the mating process.
Breakpoints can be so close to
the zero equilibrium that they are hardly relevant for elimination
(represented by the smooth transition from
the blue into the red sections of the graph).
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
Related pages:
Density-dependence & eradicability,
Uncertainties in the eradicability,
Limitation & Control.
Mathematical model.
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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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