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Full-Text Articles in Physical Sciences and Mathematics
Control Of Secondary Extinctions In Stochastic Food Webs, Dunia M. Fernandez
Control Of Secondary Extinctions In Stochastic Food Webs, Dunia M. Fernandez
Theses, Dissertations and Culminating Projects
Studies on both model-based and empirical food webs have shown that per- turbations to an ecological community can cause a species to go extinct, often resulting in the loss of additional species in a cascade of secondary extinctions. These eects can seriously debilitate a food web and threaten the existence of an ecosystem. Here, we consider niche model-based food webs with internal noise and investigate the eects of a control on a secondary extinction cas- cade triggered by a noise-induced extinction. We show that the forced removal of a nonbasal species immediately after a primary extinction can extend the mean …
Stochastic Modeling Of Zoonotic Disease, Sausan Odatalla
Stochastic Modeling Of Zoonotic Disease, Sausan Odatalla
Theses, Dissertations and Culminating Projects
We provide an overview of the mathematical modeling of deterministic and stochastic infectious disease models. These models enable one to understand the outbreak, spread, and extinction of disease. We then focus on stochastic models with a disease reservoir to understand outbreak vulnerability for zoonotic diseases such as Ebola Virus Disease (EVD). Numerical results from a more complicated EVD model are compared with the theoretical results of a simplified stochastic SISk model. We also demonstrate the effect that vaccine has on outbreak vulnerability in a population that is connected to a disease reservoir.
Simulation Based Inference In Epidemic Models, Tejitha Dharmagadda
Simulation Based Inference In Epidemic Models, Tejitha Dharmagadda
Theses, Dissertations and Culminating Projects
From ancient times to the modern day, public health has been an area of great interest. Studies on the nature of disease epidemics began around 400 BC and has been a continuous area of study for the well-being of individuals around the world. For over 100 years, epidemiologists and mathematicians have developed numerous mathematical models to improve our understanding of infectious disease dynamics with an eye on controlling and preventing disease outbreak and spread. In this thesis, we discuss several types of mathematical compartmental models such as the SIR, and SIS models. To capture the noise inherent in the real-world, …