Matching Items (2)
Description
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.
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.
ContributorsFarrell, Alexander E. (Author) / Thieme, Horst R (Thesis advisor) / Smith, Hal (Committee member) / Kuang, Yang (Committee member) / Tang, Wenbo (Committee member) / Collins, James (Committee member) / Arizona State University (Publisher)
Created2017
Description
Education of any skill based subject, such as mathematics or language, involves a significant amount of repetition and pratice. According to the National Survey of Student Engagements, students spend on average 17 hours per week reviewing and practicing material previously learned in a classroom, with higher performing students showing a tendency to spend more time practicing. As such, learning software has emerged in the past several decades focusing on providing a wide range of examples, practice problems, and situations for users to exercise their skills. Notably, math students have benefited from software that procedurally generates a virtually infinite number of practice problems and their corresponding solutions. This allows for instantaneous feedback and automatic generation of tests and quizzes. Of course, this is only possible because software is capable of generating and verifying a virtually endless supply of sample problems across a wide range of topics within mathematics. While English learning software has progressed in a similar manner, it faces a series of hurdles distinctly different from those of mathematics. In particular, there is a wide range of exception cases present in English grammar. Some words have unique spellings for their plural forms, some words have identical spelling for plural forms, and some words are conjugated differently for only one particular tense or person-of-speech. These issues combined make the problem of generating grammatically correct sentences complicated. To compound to this problem, the grammar rules in English are vast, and often depend on the context in which they are used. Verb-tense agreement (e.g. "I eat" vs "he eats"), and conjugation of irregular verbs (e.g. swim -> swam) are common examples. This thesis presents an algorithm designed to randomly generate a virtually infinite number of practice problems for students of English as a second language. This approach differs from other generation approaches by generating based on a context set by educators, so that problems can be generated in the context of what students are currently learning. The algorithm is validated through a study in which over 35 000 sentences generated by the algorithm are verified by multiple grammar checking algorithms, and a subset of the sentences are validated against 3 education standards by a subject matter expert in the field. The study found that this approach has a significantly reduced grammar error ratio compared to other generation algorithms, and shows potential where context specification is concerned.
ContributorsMoore, Zachary Christian (Author) / Amresh, Ashish (Thesis director) / Nelson, Brian (Committee member) / Software Engineering (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05