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Description
Persistence theory provides a mathematically rigorous answer to the question of population survival by establishing an initial-condition- independent positive lower bound for the long-term value of the population size. This study focuses on the persistence of discrete semiflows in infinite-dimensional state spaces that model the year-to-year dynamics of structured populations.

Persistence theory provides a mathematically rigorous answer to the question of population survival by establishing an initial-condition- independent positive lower bound for the long-term value of the population size. This study focuses on the persistence of discrete semiflows in infinite-dimensional state spaces that model the year-to-year dynamics of structured populations. The map which encapsulates the population development from one year to the next is approximated at the origin (the extinction state) by a linear or homogeneous map. The (cone) spectral radius of this approximating map is the threshold between extinction and persistence. General persistence results are applied to three particular models: a size-structured plant population model, a diffusion model (with both Neumann and Dirichlet boundary conditions) for a dispersing population of males and females that only mate and reproduce once during a very short season, and a rank-structured model for a population of males and females.
ContributorsJin, Wen (Author) / Thieme, Horst (Thesis advisor) / Milner, Fabio (Committee member) / Quigg, John (Committee member) / Smith, Hal (Committee member) / Spielberg, John (Committee member) / Arizona State University (Publisher)
Created2014
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Description
The role of climate change, as measured in terms of changes in the climatology of geophysical variables (such as temperature and rainfall), on the global distribution and burden of vector-borne diseases (VBDs) remains a subject of considerable debate. This dissertation attempts to contribute to this debate via the use of

The role of climate change, as measured in terms of changes in the climatology of geophysical variables (such as temperature and rainfall), on the global distribution and burden of vector-borne diseases (VBDs) remains a subject of considerable debate. This dissertation attempts to contribute to this debate via the use of mathematical (compartmental) modeling and statistical data analysis. In particular, the objective is to find suitable values and/or ranges of the climate variables considered (typically temperature and rainfall) for maximum vector abundance and consequently, maximum transmission intensity of the disease(s) they cause.

Motivated by the fact that understanding the dynamics of disease vector is crucial to understanding the transmission and control of the VBDs they cause, a novel weather-driven deterministic model for the population biology of the mosquito is formulated and rigorously analyzed. Numerical simulations, using relevant weather and entomological data for Anopheles mosquito (the vector for malaria), show that maximum mosquito abundance occurs when temperature and rainfall values lie in the range [20-25]C and [105-115] mm, respectively.

The Anopheles mosquito ecology model is extended to incorporate human dynamics. The resulting weather-driven malaria transmission model, which includes many of the key aspects of malaria (such as disease transmission by asymptomatically-infectious humans, and enhanced malaria immunity due to repeated exposure), was rigorously analyzed. The model which also incorporates the effect of diurnal temperature range (DTR) on malaria transmission dynamics shows that increasing DTR shifts the peak temperature value for malaria transmission from 29C (when DTR is 0C) to about 25C (when DTR is 15C).

Finally, the malaria model is adapted and used to study the transmission dynamics of chikungunya, dengue and Zika, three diseases co-circulating in the Americas caused by the same vector (Aedes aegypti). The resulting model, which is fitted using data from Mexico, is used to assess a few hypotheses (such as those associated with the possible impact the newly-released dengue vaccine will have on Zika) and the impact of variability in climate variables on the dynamics of the three diseases. Suitable temperature and rainfall ranges for the maximum transmission intensity of the three diseases are obtained.
ContributorsOkuneye, Kamaldeen O (Author) / Gumel, Abba B (Thesis advisor) / Kuang, Yang (Committee member) / Smith, Hal (Committee member) / Thieme, Horst (Committee member) / Nagy, John (Committee member) / Arizona State University (Publisher)
Created2018
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Description
In recent decades, marine ecologists have conducted extensive field work and experiments to understand the interactions between bacteria and bacteriophage (phage) in marine environments. This dissertation provides a detailed rigorous framework for gaining deeper insight into these interactions. Specific features of the dissertation include the design of a new deterministic

In recent decades, marine ecologists have conducted extensive field work and experiments to understand the interactions between bacteria and bacteriophage (phage) in marine environments. This dissertation provides a detailed rigorous framework for gaining deeper insight into these interactions. Specific features of the dissertation include the design of a new deterministic Lotka-Volterra model with n + 1 bacteria, n
+ 1 phage, with explicit nutrient, where the jth phage strain infects the first j bacterial strains, a perfectly nested infection network (NIN). This system is subject to trade-off conditions on the life-history traits of both bacteria and phage given in an earlier study Jover et al. (2013). Sufficient conditions are provided to show that a bacteria-phage community of arbitrary size with NIN can arise through the succession of permanent subcommunities, by the successive addition of one new population. Using uniform persistence theory, this entire community is shown to be permanent (uniformly persistent), meaning that all populations ultimately survive.

It is shown that a modified version of the original NIN Lotka-Volterra model with implicit nutrient considered by Jover et al. (2013) is permanent. A new one-to-one infection network (OIN) is also considered where each bacterium is infected by only one phage, and that phage infects only that bacterium. This model does not use the trade-offs on phage infection range, and bacterium resistance to phage. The OIN model is shown to be permanent, and using Lyapunov function theory, coupled with LaSalle’s Invariance Principle, the unique coexistence equilibrium associated with the NIN is globally asymptotically stable provided that the inter- and intra-specific bacterial competition coefficients are equal across all bacteria.

Finally, the OIN model is extended to a “Kill the Winner” (KtW) Lotka-Volterra model

of marine communities consisting of bacteria, phage, and zooplankton. The zooplankton

acts as a super bacteriophage, which infects all bacteria. This model is shown to be permanent.
ContributorsKorytowski, Daniel (Author) / Smith, Hal (Thesis advisor) / Gumel, Abba (Committee member) / Kuang, Yang (Committee member) / Gardner, Carl (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2016
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Description
The non-native mosquito Aedes aegypti has become a common nuisance in Maricopa county. Associated with human settlement, Ae. aegypti is known to reproduce in standing water sources both indoors and outdoors, within vessels such as tires, flowerpots, and neglected swimming pools (Jansen & Beebe, 2010). Ae. aegypti and the related

The non-native mosquito Aedes aegypti has become a common nuisance in Maricopa county. Associated with human settlement, Ae. aegypti is known to reproduce in standing water sources both indoors and outdoors, within vessels such as tires, flowerpots, and neglected swimming pools (Jansen & Beebe, 2010). Ae. aegypti and the related Ae. albopictus are the primary vectors of the arboviral diseases chikungunya, Zika, yellow fever and dengue. Ae. aegypti tends to blood feed multiple times per gonotrophic cycle (cycle of feeding and egg laying) which, alongside a preference for human blood and close association with human habitation, contributes to an increased risk of Ae. aegypti borne virus transmission (Scott & Takken, 2012). Between 2010-2017, 153 travel-associated cases of dengue were reported in the whole of Arizona (Rivera et al., 2020); while there have been no documented locally transmitted cases of Aedes borne diseases in Maricopa county, there are no apparent reasons why local transmission can’t occur in the future via local Aedes aegypti mosquitoes infected after feeding from travelling viremic hosts. Incidents of local dengue transmission in New York (Rivera et al., 2020) and Barcelona (European Center for Disease Control [ECDC], 2019) suggest that outbreaks of Aedes borne arbovirus’ can occur in regions more temperate than the current endemic range of Aedes borne diseases. Further, while the fact that Ae. aegypti eggs have a high mortality rate when exposed to cold temperatures limits the ability for Ae aegypti to establish stable breeding populations in temperate climates (Thomas, Obermayr, Fischer, Kreyling, & Beierkuhnlein, 2012), global increases in temperature will expand the possible ranges of Ae aegypti and Aedes borne diseases.
ContributorsHon, Ruiheng (Author) / Paaijmans, Krijn (Thesis director) / Bond, Angela (Committee member) / Angilletta, Michael (Committee member) / School of Molecular Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05