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Density-dependence
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We assume that regulatory processes within the host-parasite relationship
are an evolutionary result, originating from the necessity for an infectious agent
to persist in hosts without affecting them too much,
or killing them. Mathematical models help to
understand the effects these processes have on the eradicability of
the infection.
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In the parasitological context, the term "density-dependence" describes non-linear
relationships between the densities of parasite stages within the life-cycle.
Here, "density" is the parasite number per host, per vector, per volume of blood,
or per any other unit of interest.
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We discriminate the two cases of limitation and facilitation:
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Limitation is associated with the fact that no population can grow indefinitely.
E.g. the number of parasites per host is limited by the size or the death of the host.
If we relate the density of parasite stage x to the preceding parasite stage x-1,
then the density of x achieves a maximum with inceasing density of x-1, i.e. the relationship saturates.
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Facilitation describes the opposite: as the density of the parasite stage x-1 inceases,
the density of the parasite stage x increases over-proportionally.
As in the case of limitation, such a process cannot grow indefinately and thus,
faciliation processes must proceed with a limitation process.
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