Graduate Theses & Dissertations

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Stability Properties of Disease Models under Economic Expectations
Comprehending the dynamics of infectious diseases is very important in formulating public health policies to tackling their prevalence. Mathematical epidemiology (ME) has played a very vital role in achieving the above. Nevertheless, classical mathematical epidemiological models do not explicitly model the behavioural responses of individuals in the presence of prevalence of these diseases. Economic epidemiology (EE) as a field has stepped in to fill this gap by integrating economic and mathematical concepts within one framework. This thesis investigated two issues in this area. The methods employed are the standard linear analysis of stability of dynamical systems and numerical simulation. Below are the investigations and the findings of this thesis: Firstly, an investigation into the stability properties of the equilibria of EE models is carried out. We investigated the stability properties of modified EE systems studied by Aadland et al. [6] by introducing a parametric quadratic utility function into the model, thus making it possible to model the maximum number of contacts made by rational individuals to be determined by a parameter. This parameter in particular influences the level of utility of rational individuals. We have shown that if rational individuals have a range of possible contacts to choose from, with the maximum of the number of contacts allowable for these individuals being dependent on a parameter, the variation in this parameter tends to affect the stability properties of the system. We also showed that under the assumption of permanent recovery for disease coupled with individuals observing or not observing their immunity, death and birth rates can affect the stability of the system. These parameters also have effect on the dynamics of the EE SIS system. Secondly, an EE model of syphilis infectivity among &ldquo men who have sex with men &rdquo (MSM) in detention centres is developed in an attempt at looking at the effect of behavioural responses on the disease dynamics among MSM. This was done by explicitly incorporating the interplay of the biology of the disease and the behaviour of the inmates. We investigated the stability properties of the system under rational expectations where we showed that: (1) Behavioural responses to the prevalence of the disease affect the stability of the system. Therefore, public health policies have the tendency of putting the system on indeterminate paths if rational MSM have complete knowledge of the laws governing the motion of the disease states as well as a complete understanding on how others behave in the system when faced with risk-benefit trade-offs. (2) The prevalence of the disease in the long run is influenced by incentives that drive the utility of the MSM inmates. (3) The interplay between the dynamics of the biology of the disease and the behavioural responses of rational MSM tends to put the system at equilibrium quickly as compared to its counterpart (that is when the system is solely dependent on the biology of the disease) when subjected to small perturbation. Author Keywords: economic and mathematical epidemiology models, explosive path, indeterminate-path stability, numerical solution, health gap, saddle-path stability, syphilis,
Calving site selection and fidelity in a restored elk (Cervus elaphus) herd in Bancroft, Ontario, Canada
ABSTRACT Calving site selection and fidelity in a restored elk (Cervus elaphus) herd in Bancroft Ontario, Canada. Michael R. Allan Parturition site selection by ungulates is believed to be influenced by forage abundance and concealment from predators. In 2011 and 2012, I used vaginal implant transmitters and movements to identify calving sites for 23 GPS collared elk (Cervus elaphus) from a restored herd. I tested the hypothesis that maternal elk used sites with higher forage and denser concealment compared to pre-calving sites at micro and macrohabitat levels. I detected no significant microhabitat differences from direct measurements of vegetation. At the macrohabitat scale, based on proximity of landcover classes, mean distances to hardwood forests was significantly less for calving (153 m) than pre-calving sites (198 m). Site fidelity is hypothesized to offer security in terms of familiarity to an area. I tested the hypothesis that females demonstrated fidelity to their previous year's location during pre-partum, parturition, post partum, breeding and winter periods. Elk were more philopatric during parturition and post partum than during breeding. Compared to winter elk were more philopatric during pre-partum, parturition and post-partum periods. Expressed as distance between consecutive-year calving locations, site fidelity varied with 27% of females exhibiting high (<1 km), 18% moderate and 55% (>2.9 km) low fidelity. I measured nearest-neighbour distances at calving time, exploring the hypothesis that females distance themselves from conspecifics. Elk increased the average distances to collared conspecifics during parturition; however, sample sizes were small. This strategy might influence calving site selection. Rapid movement prior to parturition, low site fidelity and spacing-out of females during parturition appear to be strategies to minimize predator risk and detection. Little evidence of selection for vegetation structure suggests this may not be limiting to these elk. Author Keywords: calving, elk, fidelity, movement, parturition, selection
Effect of SP600125 JNK Inhibitor on Cadmium-Treated Mouse Embryo Forelimb Bud Cells In Vitro
This study investigated the role of the JNK signaling pathway in cadmium-treated mouse embryo forelimb bud cells in vitro. Primary cultures of forelimb bud cells harvested at day 11 of gestation were pre-treated with JNK inhibitor SP600125, and incubated with or without CdCl2 for 15, 30, 60, 120 minutes and 24, 48 hours or 5 days. Endpoints of toxicity were measured through cell differentiation by Alcian Blue Assay and phosphorylation of JNK proteins by Western blot. The results demonstrated that, in the cell differentiation assay, inhibiting JNK activation by 20 μM SP600125 causes an enhanced toxic effect in limb cells and inhibits cell differentiation, whereas 2 μM decreases differentiated nodule numbers under both cadmium stress and normal conditions. In conclusion, the JNK pathway has an essential role in the differentiation processes of limb bud cells in normal growth conditions. Author Keywords: Cadmium, Cell Signaling, JNK, Limbs, Mouse Embryo, Teratology
Spatial Dynamics of Wind Pollination in Broadleaf Cattail (Typha latifolia)
Natural populations of flowering plants rarely have perfectly uniform distributions, so trends in pollen dispersal should affect the size of the pollination neighbourhood and influence mating opportunities. Here I used spatial analysis to determine the size of the pollination neighbourhood in a stand of the herbaceous, wind-pollinated plant (Typha latifolia; broad-leaved cattail) by evaluating patterns of pollen production and seed set by individual cattail shoots. I found a positive correlation between pollen production and seed set among near-neighbour shoots (i.e., within 4 m2 patches of the stand; Pearson's r = 0.235, p < 0.05, df = 77) that was not driven by a correlation between these variables within inflorescences (Pearson's r = 0.052, p > 0.45, df = 203). I also detected significant spatial autocorrelations in seed set over short distances (up to ~ 5 m) and a significant cross-correlation between pollen production and seed set over distances of < 1 m indicating that the majority of pollination events involve short distances. Patterns of pollen availability were simulated to explore the shape of the pollen dispersal curve. Simulated pollen availability fit actual patterns of seed set only under assumptions of highly restricted pollen dispersal. Together, these findings indicate that even though Typha latifolia produces copious amounts of pollen, the vast majority of pollen dispersal was highly localized to distances of ~ 1 m. Moreover, although Typha latifolia is self-compatible and has been described as largely selfing, my results are more consistent with the importance of pollen transfer between nearby inflorescences. Therefore, realized selfing rates of Typha latifolia should largely depend on the clonal structure of populations. Author Keywords: clonal structure, correlogram, dispersal curves, pollination, spatial analysis, Typha latifolia

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