The success of social insects is dependent upon cooperative behavior and adaptive strategies shaped by natural selection that respond to internal or external conditions. The objective of my research was to investigate specific mechanisms that have helped shaped the structure of division of labor observed in social insect colonies, including age polyethism and nutrition, and phenomena known to increase colony survival such as egg cannibalism. I developed various Ordinary Differential Equation (ODE) models in which I applied dynamical, bifurcation, and sensitivity analysis to carefully study and visualize biological outcomes in social organisms to answer questions regarding the conditions under which a colony can survive. First, I investigated how the population and evolutionary dynamics of egg cannibalism and division of labor can promote colony survival. I then introduced a model of social conflict behavior to study the inclusion of different response functions that explore the benefits of cannibalistic behavior and how it contributes to age polyethism, the change in behavior of workers as they age, and its biological relevance. Finally, I introduced a model to investigate the importance of pollen nutritional status in a honeybee colony, how it affects population growth and influences division of labor within the worker caste. My results first reveal that both cannibalism and division of labor are adaptive strategies that increase the size of the worker population, and therefore, the persistence of the colony. I show the importance of food collection, consumption, and processing rates to promote good colony nutrition leading to the coexistence of brood and adult workers. Lastly, I show how taking into account seasonality for pollen collection improves the prediction of long term consequences.
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.
Many coastal cities around the world are becoming increasingly vulnerable to natural disasters, particularly flooding driven by tropical storm and hurricane storm surge – typically the most destructive feature of these storms, generating significant economic damage and loss of life. This increase in vulnerability is driven by the interactions between a wide number of complex social and climatic factors, including population growth, irresponsible urban development, a decrease in essential service provision, sea level rise, and changing storm regimes. These issues are exacerbated by the short-term strategic planning that dominates political action and economic decision-making, resulting in many vulnerable coastal communities being particularly unprepared for large, infrequent storm surge events. This lack of preparedness manifests in several ways, but one of the most visible is the lack of comprehensive evacuation and rescue operation plans for use after major storm surge flooding occurs. Typical evacuation or rescue plans are built using a model of a region’s intact road network. While useful for pre-disaster purposes, the immediate aftermath of large floods sees enormous swaths of a given region’s road system flooded, rendering most of these plans largely useless. Post-storm evacuation and rescue requires large amounts of atypical travel through a region (i.e., across non-road surfaces). Traditional road network models (such as those that are used to generate evacuation routes) are unable to conceptualize this type of transportation, and so are of limited utility during post-disaster scenarios. To solve these problems, this dissertation introduces an alternative network conceptualization that preserves important on-network information but also accounts for the possibility of off-network travel during a disaster. Providing this in situ context is necessary to adequately model transportation through a post-storm landscape, one in which evacuees and rescuers are regularly departing from roads and one in which many roads are completely interdicted by flooding. This modeling approach is used to automatically generate routes through a flooded coastal urban area, as well as to identify potentially critical road segments in advance of an actual storm. These tools may help both emergency managers better prepare for large storms, and urban planners in their efforts to mitigate flood damage.
Environmental heat is a growing concern in cities as a consequence of rapid urbanization and climate change, threatening human health and urban vitality. The transportation system is naturally embedded in the issue of urban heat and human heat exposure. Research has established how heat poses a threat to urban inhabitants and how urban infrastructure design can lead to increased urban heat. Yet there are gaps in understanding how urban communities accumulate heat exposure, and how significantly the urban transportation system influences or exacerbates the many issues of urban heat. This dissertation focuses on advancing the understanding of how modern urban transportation influences urban heat and human heat exposure through three research objectives: 1) Investigate how human activity results in different outdoor heat exposure; 2) Quantify the growth and extent of urban parking infrastructure; and 3) Model and analyze how pavements and vehicles contribute to urban heat.
In the urban US, traveling outdoors (e.g. biking or walking) is the most frequent activity to cause heat exposure during hot periods. However, outdoor travel durations are often very short, and other longer activities such as outdoor housework and recreation contribute more to cumulative urban heat exposure. In Phoenix, parking and roadway pavement infrastructure contributes significantly to the urban heat balance, especially during summer afternoons, and vehicles only contribute significantly in local areas with high density rush hour vehicle travel. Future development of urban areas (especially those with concerns of extreme heat) should focus on ensuring access and mobility for its inhabitants without sacrificing thermal comfort. This may require urban redesign of transportation systems to be less auto-centric, but without clear pathways to mitigating impacts of urban heat, it may be difficult to promote transitions to travel modes that inherently necessitate heat exposure. Transportation planners and engineers need to be cognizant of the pathways to increased urban heat and human heat exposure when planning and designing urban transportation systems.
A mathematical model is developed for the spread of rabies in a spatially distributed fox population to model the spread of the rabies epizootic through middle Europe that occurred in the second half of the 20th century. The model considers both territorial and wandering rabid foxes and includes a latent period for the infection. Since the model assumes these two kinds of rabid foxes, it is a system of both partial differential and integral equations (with integration
over space and, occasionally, also over time). To study the spreading speeds of the rabies epidemic, the model is reduced to a scalar Volterra-Hammerstein integral equation, and space-time Laplace transform of the integral equation is used to derive implicit formulas for the spreading speed. The spreading speeds are discussed and implicit formulas are given for latent periods of fixed length, exponentially distributed length, Gamma distributed length, and log-normally distributed length. A number of analytic and numerical results are shown pertaining to the spreading speeds.
Further, a numerical algorithm is described for the simulation
of the spread of rabies in a spatially distributed fox population on a bounded domain with Dirichlet boundary conditions. I propose the following methods for the numerical approximation of solutions. The partial differential and integral equations are discretized in the space variable by central differences of second order and by
the composite trapezoidal rule. Next, the ordinary or delay differential equations that are obtained this way are discretized in time by explicit
continuous Runge-Kutta methods of fourth order for ordinary and delay differential systems. My particular interest
is in how the partition of rabid foxes into
territorial and diffusing rabid foxes influences
the spreading speed, a question that can be answered by purely analytic means only for small basic reproduction numbers. I will restrict the numerical analysis
to latent periods of fixed length and to exponentially
distributed latent periods.
The results of the numerical calculations
are compared for latent periods
of fixed and exponentially distributed length
and for various proportions of territorial
and wandering rabid foxes.
The speeds of spread observed in the
simulations are compared
to spreading speeds obtained by numerically solving the analytic formulas
and to observed speeds of epizootic frontlines
in the European rabies outbreak 1940 to 1980.
This study investigated the effect of environmental heat stress on physiological and performance measures during a ~4 mi time trial (TT) mountain hike in the Phoenix metropolitan area. Participants (n = 12; 7M/5F; age 21.6 ± 2.47 [SD]) climbed ‘A’ mountain (~1 mi) four times on a hot day (HOT; wet bulb globe temperature [WBGT] = 31.6°C) and again on a moderate day (MOD; WBGT = 19.0°C). Physiological and performance measures were made before and throughout the course of each hike. Mean pre-hike hydration status (urine specific gravity [USG]) indicated that participants began both HOT and MOD trials in a euhydrated state (1.016 ± 0.010 and 1.010 ± 0.008, respectively) and means did not differ significantly between trials (p = .085). Time trial performance was impaired by -11% (11.1 minutes) in the HOT trial (105 ± 21.7 min), compared to MOD (93.9 ± 13.1 min) (p = .013). Peak core temperatures were significantly higher in HOT (38.5 ± 0.36°C) versus MOD (38.0 ± 0.30°C) with progressively increasing differences between trials over time (p < .001). Peak ratings of perceived exertion were significantly higher in HOT (14.2 ± 2.38) compared to MOD (11.9 ± 2.02) (p = .007). Relative intensity (percent of age-predicted maximal heart rate [HR]), estimated absolute intensity (metabolic equivalents [METs]), and estimated energy expenditure (MET-h) were all increased in HOT, but not significantly so. The HOT condition reduced predicted maximal aerobic capacity (CRFp) by 6% (p = .026). Sweat rates differed significantly between HOT (1.38 ± 0.53 L/h) and MOD (0.84 ± 0.27 L/h) (p = .01). Percent body mass loss (PBML) did not differ significantly between HOT (1.06 ± 0.95%) and MOD (0.98 ± 0.84%) (p = .869). All repeated measures variables showed significant between-subjects effects (p < .05), indicating individual differences in response to test conditions. Heat stress was shown to negatively affect physiological and performance measures in recreational mountain hikers. However, considerable variation exists between individuals, and the degree of physiological and performance impairment is probably due, in part, to differences in aerobic fitness and acclimatization status rather than pre- or during-performance hydration status.
An algebraic representation of the nucleotide bases is developed. This algebraic representation makes it possible to convert nucleotide sequences into algebraic sequences, apply mathematical ideas and convert results back into nucleotide terms. Using the algebra developed, a mapping is found from the naturally-occurring codons to an alternative set of codons which makes genes constructed from them mutation-tolerant, provided no more than one substitution mutation occurs per codon. The ideas discussed naturally extend to finding codons that can tolerate t arbitrarily chosen number of mutations per codon. Finally, random substitution events are simulated in both a wild-type green fluorescent protein (GFP) gene and its mutol variant and the amino acid sequence expressed from each post-mutation is compared with the amino acid sequence pre-mutation.
This work assumes the existence of synthetic protein-assembling entities that function like tRNAs but can read k nucleotides at a time, with k greater than or equal to 5. The realization of this assumption is presented as a challenge to the research community.
This dissertation is structured as a growing tumor. Chapters 2 and 3 consider spheroid models. These models are adept at describing 'early-time' tumors, before the tumor needs to co-opt blood vessels to continue sustained growth. I consider two partial differential equation (PDE) models for spheroid growth of glioblastoma. I compare these models to in vitro experimental data for glioblastoma tumor cell lines and other proposed models. Further, I investigate the conditions under which traveling wave solutions exist and confirm numerically.
As a tumor grows, it can no longer be approximated by a spheroid, and it becomes necessary to use in vivo data and more sophisticated modeling to model the growth and diffusion. In Chapter 4, I explore experimental data and computational models for describing growth and diffusion of glioblastoma in murine brains. I discuss not only how the data was obtained, but how the 3D brain geometry is created from Magnetic Resonance (MR) images. A 3D finite-difference code is used to model tumor growth using a basic reaction-diffusion equation. I formulate and test hypotheses as to why there are large differences between the final tumor sizes between the mice.
Once a tumor has reached a detectable size, it is diagnosed, and treatment begins. Chapter 5 considers modeling the treatment of prostate cancer. I consider a joint model with hormonal therapy as well as immunotherapy. I consider a timing study to determine whether changing the vaccine timing has any effect on the outcome of the patient. In addition, I perform basic analysis on the six-dimensional ordinary differential equation (ODE). I also consider the limiting case, and perform a full global analysis.