The purpose of this thesis is to determine whether Tai Chi Qigong or Health Information podcasts are more effective for improving mental health and sleep outcomes for midlife women with mobility impairments. No other studies have been done to investigate whether Tai Chi can be more effective for sleep, depressive symptoms, and anxiety for midlife women with mobility impairments specifically. Overall, it was found that midlife women with mobility impairments experienced better sleep when they focused on health information podcasts in comparison to Tai Chi. Change in anxiety and depressive symptoms were negligible.
The purpose of this thesis is to determine whether Tai Chi Qigong or Health Information podcasts are more effective for improving mental health and sleep outcomes for midlife women with mobility impairments. No other studies have been done to investigate whether Tai Chi can be more effective for sleep, depressive symptoms, and anxiety for midlife women with mobility impairments specifically. Overall, it was found that midlife women with mobility impairments experienced better sleep when they focused on health information podcasts in comparison to Tai Chi. Change in anxiety and depressive symptoms were negligible.
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.
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.