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Articles 1 - 4 of 4
Full-Text Articles in Applied Mathematics
Use Of Kalman Filtering In State And Parameter Estimation Of Diabetes Models, Cassidy Le
Use Of Kalman Filtering In State And Parameter Estimation Of Diabetes Models, Cassidy Le
HMC Senior Theses
Diabetes continues to affect many lives every year, putting those affected by it at higher risk of serious health issues. Despite many efforts, there currently is no cure for diabetes. Nevertheless, researchers continue to study diabetes in hopes of understanding the disease and how it affects people, creating mathematical models to simulate the onset and progression of diabetes. Recent research by David J. Albers, Matthew E. Levine, Andrew Stuart, Lena Mamykina, Bruce Gluckman, and George Hripcsak1 has suggested that these models can be furthered through the use of Data Assimilation, a regression method that synchronizes a model with a …
Mathematical Modeling Of Blood Coagulation, Joana L. Perdomo
Mathematical Modeling Of Blood Coagulation, Joana L. Perdomo
HMC Senior Theses
Blood coagulation is a series of biochemical reactions that take place to form a blood clot. Abnormalities in coagulation, such as under-clotting or over- clotting, can lead to significant blood loss, cardiac arrest, damage to vital organs, or even death. Thus, understanding quantitatively how blood coagulation works is important in informing clinical decisions about treating deficiencies and disorders. Quantifying blood coagulation is possible through mathematical modeling. This review presents different mathematical models that have been developed in the past 30 years to describe the biochemistry, biophysics, and clinical applications of blood coagulation research. This review includes the strengths and limitations …
Noise, Delays, And Resonance In A Neural Network, Austin Quan
Noise, Delays, And Resonance In A Neural Network, Austin Quan
HMC Senior Theses
A stochastic-delay differential equation (SDDE) model of a small neural network with recurrent inhibition is presented and analyzed. The model exhibits unexpected transient behavior: oscillations that occur at the boundary of the basins of attraction when the system is bistable. These are known as delay-induced transitory oscillations (DITOs). This behavior is analyzed in the context of stochastic resonance, an unintuitive, though widely researched phenomenon in physical bistable systems where noise can play in constructive role in strengthening an input signal. A method for modeling the dynamics using a probabilistic three-state model is proposed, and supported with numerical evidence. The potential …
Mathematical Aids Epidemic Model: Preferential Anti-Retroviral Therapy Distribution In Resource Constrained Countries, Nadia Abuelezam
Mathematical Aids Epidemic Model: Preferential Anti-Retroviral Therapy Distribution In Resource Constrained Countries, Nadia Abuelezam
HMC Senior Theses
HIV/AIDS is one of the largest health problems the world is currently facing. Even with anti-retroviral therapies (ART), many resource-constrained countries are unable to meet the treatment needs of their infected populations. ART-distribution methods need to be created that prevent the largest number of future HIV infections. We have developed a compartment model that tracks the spread of HIV in multiple two-sex populations over time in the presence of limited treatment. The model has been fit to represent the HIV epidemic in rural and urban areas in Uganda. With the model we examine the spread of HIV among urban and …