abstract: Using a simple $SI$ infection model, I uncover the
overall dynamics of the system and how they depend on the incidence
function. I consider both an epidemic and endemic perspective of the
model, but in both cases, three classes of incidence
functions are identified.
In the epidemic form,
power incidences, where the infective portion $I^p$ has $p\in(0,1)$,
cause unconditional host extinction,
homogeneous incidences have host extinction for certain parameter constellations and
host survival for others, and upper density-dependent incidences
never cause host extinction. The case of non-extinction in upper
density-dependent
incidences extends to the case where a latent period is included.
Using data from experiments with rhanavirus and salamanders,
maximum likelihood estimates are applied to the data.
With these estimates,
I generate the corrected Akaike information criteria, which
reward a low likelihood and punish the use of more parameters.
This generates the Akaike weight, which is used to fit
parameters to the data, and determine which incidence functions
fit the data the best.
From an endemic perspective, I observe
that power incidences cause initial condition dependent host extinction for
some parameter constellations and global stability for others,
homogeneous incidences have host extinction for certain parameter constellations and
host survival for others, and upper density-dependent incidences
never cause host extinction.
The dynamics when the incidence function is homogeneous are deeply explored.
I expand the endemic considerations in the homogeneous case
by adding a predator into the model.
Using persistence theory, I show the conditions for the persistence of each of the
predator, prey, and parasite species. Potential dynamics of the system include parasite mediated
persistence of the predator, survival of the ecosystem at high initial predator levels and
ecosystem collapse at low initial predator levels, persistence of all three species, and much more. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2017
| Identifer | oai:union.ndltd.org:asu.edu/item:44062 |
| Date | January 2017 |
| Contributors | Farrell, Alex Patrick (Author), Thieme, Horst R (Advisor), Smith, Hal (Committee member), Kuang, Yang (Committee member), Tang, Wenbo (Committee member), Collins, James (Committee member), Arizona State University (Publisher) |
| Source Sets | Arizona State University |
| Language | English |
| Detected Language | English |
| Type | Doctoral Dissertation |
| Format | 238 pages |
| Rights | http://rightsstatements.org/vocab/InC/1.0/, All Rights Reserved |
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