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Full-Text Articles in Physical Sciences and Mathematics
Discrete Epidemic Models With Arbitrarily Distributed Disease Stages, Nancy Hernandez Ceron
Discrete Epidemic Models With Arbitrarily Distributed Disease Stages, Nancy Hernandez Ceron
Open Access Dissertations
The use of discrete-time models (or discrete models) in the field of mathematical epidemiology has been limited while continuous-time models (or continuous models) are often times preferred, particularly because disease dynamics do occur continuously in time and more mathematical tools are available for model analysis. How- ever, discrete models are not only more tractable and easier to understand, but also more directly related to data, particularly when the disease stage distributions are arbitrarily distributed (e.g., when the data cannot be fitted by distributions from a parametric family). Under these circumstances continuous models usually lead to complex system of integral equations. …
Mathematical Approaches To Food Nutrient Content Estimation With A Focus On Phenylalanine, Jieun Kim
Mathematical Approaches To Food Nutrient Content Estimation With A Focus On Phenylalanine, Jieun Kim
Open Access Dissertations
Managing the intake of a certain nutrient can be an effective treatment for some inherited metabolic disorders. An example of such dietary treatments is for phenylketonuria (PKU), for which patients must follow a low-phenylalanine diet for life. Some food databases provide the phenylalanine (Phe) content for a large number of unprocessed foods, and a limited number of composite foods; however, they are not exhaustive. As an attempt to complete this list, we introduce three mathematical approaches to estimate a bound for the Phe content based on the available nutritional information. The first approach is based on the statistical distribution of …