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Chapter 1 provides background information and motivation for infectious disease forecasting and outlines the rest of the thesis.
In chapter 2, logistic patch models are used to assess and forecast the 2013-2015 West Africa Zaire ebolavirus epidemic. In particular, this chapter is concerned with comparing and contrasting the effects that spatial heterogeneity has on the forecasting performance of the cumulative infected case counts reported during the epidemic.
In chapter 3, two simple phenomenological models inspired from population biology are used to assess the Research and Policy for Infectious Disease Dynamics (RAPIDD) Ebola Challenge; a simulated epidemic that generated 4 infectious disease scenarios. Because of the nature of the synthetically generated data, model predictions are compared to exact epidemiological quantities used in the simulation.
In chapter 4, these models are applied to the 1904 Plague epidemic that occurred in Bombay. This chapter provides evidence that these simple models may be applicable to infectious diseases no matter the disease transmission mechanism.
Chapter 5, uses the patch models from chapter 2 to explore how migration in the 1904 Plague epidemic changes the final epidemic size.
The final chapter is an interdisciplinary project concerning within-host dynamics of cereal yellow dwarf virus-RPV, a plant pathogen from a virus group that infects over 150 grass species. Motivated by environmental nutrient enrichment due to anthropological activities, mathematical models are employed to investigate the relevance of resource competition to pathogen and host dynamics.
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Trees serve as a natural umbrella to mitigate insolation absorbed by features of the urban environment, especially building structures and pavements. For a desert community, trees are a particularly valuable asset because they contribute to energy conservation efforts, improve home values, allow for cost savings, and promote enhanced health and well-being. The main obstacle in creating a sustainable urban community in a desert city with trees is the scarceness and cost of irrigation water. Thus, strategically located and arranged desert trees with the fewest tree numbers possible potentially translate into significant energy, water and long-term cost savings as well as conservation, economic, and health benefits. The objective of this dissertation is to achieve this research goal with integrated methods from both theoretical and empirical perspectives.
This dissertation includes three main parts. The first part proposes a spatial optimization method to optimize the tree locations with the objective to maximize shade coverage on building facades and open structures and minimize shade coverage on building rooftops in a 3-dimensional environment. Second, an outdoor urban physical scale model with field measurement is presented to understand the cooling and locational benefits of tree shade. The third part implements a microclimate numerical simulation model to analyze how the specific tree locations and arrangements influence outdoor microclimates and improve human thermal comfort. These three parts of the dissertation attempt to fill the research gap of how to strategically locate trees at the building to neighborhood scale, and quantifying the impact of such arrangements.
Results highlight the significance of arranging residential shade trees across different geographical scales. In both the building and neighborhood scales, research results recommend that trees should be arranged in the central part of the building south front yard. More cooling benefits are provided to the building structures and outdoor microclimates with a cluster tree arrangement without canopy overlap; however, if residents are interested in creating a better outdoor thermal environment, open space between trees is needed to enhance the wind environment for better human thermal comfort. Considering the rapid urbanization process, limited water resources supply, and the severe heat stress in the urban areas, judicious design and planning of trees is of increasing importance for improving the life quality and sustaining the urban environment.
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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.
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This dissertation proposes two PageRank-based analytical methods, Pathways of Topological Rank Analysis (PoTRA) and miR2Pathway, discussed in Chapter 1 and Chapter 2, respectively. PoTRA focuses on detecting pathways with an altered number of hub genes in corresponding pathways between two phenotypes. The basis for PoTRA is that the loss of connectivity is a common topological trait of cancer networks, as well as the prior knowledge that a normal biological network is a scale-free network whose degree distribution follows a power law where a small number of nodes are hubs and a large number of nodes are non-hubs. However, from normal to cancer, the process of the network losing connectivity might be the process of disrupting the scale-free structure of the network, namely, the number of hub genes might be altered in cancer compared to that in normal samples. Hence, it is hypothesized that if the number of hub genes is different in a pathway between normal and cancer, this pathway might be involved in cancer. MiR2Pathway focuses on quantifying the differential effects of miRNAs on the activity of a biological pathway when miRNA-mRNA connections are altered from normal to disease and rank disease risk of rewired miRNA-mediated biological pathways. This dissertation explores how rewired gene-gene interactions and rewired miRNA-mRNA interactions lead to aberrant activity of biological pathways, and rank pathways for their disease risk. The two methods proposed here can be used to complement existing genomics analysis methods to facilitate the study of biological mechanisms behind disease at the systems-level.
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Chapter 2 focuses sorely on time where the escape of a generic cancer out of immune control is described by stochastic delayed differential equations (SDDEs). Without time delay and noise, this system demonstrates bistability. The effects of response time of the immune system and stochasticity in the tumor proliferation rate are studied by including delay and noise in the model. Stability, persistence and extinction of the tumor are analyzed. The result shows that both time delay and noise can induce the transition from low tumor burden equilibrium to high tumor equilibrium. The aforementioned work has been published (Han et al., 2019b).
In Chapter 3, Glioblastoma multiforme (GBM) is studied using a partial differential equation (PDE) model. GBM is an aggressive brain cancer with a grim prognosis. A mathematical model of GBM growth with explicit motility, birth, and death processes is proposed. A novel method is developed to approximate key characteristics of the wave profile, which can be compared with MRI data. Several test cases of MRI data of GBM patients are used to yield personalized parameterizations of the model. The aforementioned work has been published (Han et al., 2019a).
Chapter 4 presents an innovative way of forecasting spatial cancer invasion. Most mathematical models, including the ones described in previous chapters, are formulated based on strong assumptions, which are hard, if not impossible, to verify due to complexity of biological processes and lack of quality data. Instead, a nonparametric forecasting method using Gaussian processes is proposed. By exploiting the local nature of the spatio-temporal process, sparse (in terms of time) data is sufficient for forecasting. Desirable properties of Gaussian processes facilitate selection of the size of the local neighborhood and computationally efficient propagation of uncertainty. The method is tested on synthetic data and demonstrates promising results.
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changes in the diffusion, growth, and death parameters was performed, in order to find a set of parameter values that accurately model observed tumor growth for a given patient. Additional changes were made to the diffusion parameters to account for the arrangement of nerve tracts in the brain, resulting in varying rates of diffusion. In general, small changes in the growth rates had a large impact on the outcome of the simulations, and for each patient there exists a set of parameters that allow the model to simulate a tumor that matches observed tumor growth in the patient over a period of two or three months. Furthermore, these results are more accurate with anisotropic diffusion, rather than isotropic diffusion. However, these parameters lead to inaccurate results for patients with tumors that undergo no observable growth over the given time interval. While it is possible to simulate long-term tumor growth, the simulation requires multiple comparisons to available MRI scans in order to find a set of parameters that provide an accurate prognosis.
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