Open Access. Powered by Scholars. Published by Universities.®
Ordinary Differential Equations and Applied Dynamics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Institution
- Keyword
-
- Differential equations (2)
- HIV (2)
- Human immunodeficiency virus (2)
- Mathematical modeling (2)
- T cells (2)
-
- Treatment-resistant mutations (2)
- Aedes aegypti (1)
- Biological modeling (1)
- Cholera (1)
- Confidence Intervals (1)
- Dengue (1)
- Diabetic Foot Ulcer (1)
- Disease modeling, Cape Verde (1)
- Disease-free equilibrium (1)
- Dynamics (1)
- Endemic equilibrium (1)
- Epidemiology (1)
- Infectious disease (1)
- Itô stochastic differential equation (1)
- Kinetics (1)
- Migration (1)
- Multiple patches (1)
- Namics (1)
- Optimal control (1)
- Phototransduction (1)
- Prediction Intervals (1)
- Probability of extinction (1)
- Rod photoreceptors (1)
- SE-optimal (1)
- Single-photon responses (1)
Articles 1 - 7 of 7
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Multipatch Stochastic Epidemic Model For The Dynamics Of A Tick-Borne Disease, Milliward Maliyoni, Holly D. Gaff, Keshlan S. Govinder, Faraimunashe Chirove
Multipatch Stochastic Epidemic Model For The Dynamics Of A Tick-Borne Disease, Milliward Maliyoni, Holly D. Gaff, Keshlan S. Govinder, Faraimunashe Chirove
Biological Sciences Faculty Publications
Spatial heterogeneity and migration of hosts and ticks have an impact on the spread, extinction and persistence of tick-borne diseases. In this paper, we investigate the impact of between-patch migration of white-tailed deer and lone star ticks on the dynamics of a tick-borne disease with regard to disease extinction and persistence using a system of Itô stochastic differential equations model. It is shown that the disease-free equilibrium exists and is unique. The general formula for computing the basic reproduction number for all patches is derived. We show that for patches in isolation, the basic reproduction number is equal to the …
A Study Of Cholera Transmission, Urmi Ghosh-Dastidar
A Study Of Cholera Transmission, Urmi Ghosh-Dastidar
Open Educational Resources
A recent cholera outbreak in Haiti brought public attention to this disease. Cholera, a diarrheal disease, is caused by an intestinal bacterium, and if not addressed in a timely manner may become fatal. During the project described here, the students will learn how to solve and address a practical problem such as cholera transmission using various mathematical tools. Students will learn to develop a differential equation model based on practical scenarios, analyze the model using mathematics as well as numerical simulation, and finally describe the results in words that are understandable by the people who are not specialists in this …
Parameter Estimation And Optimal Design Techniques To Analyze A Mathematical Model In Wound Healing, Nigar Karimli
Parameter Estimation And Optimal Design Techniques To Analyze A Mathematical Model In Wound Healing, Nigar Karimli
Masters Theses & Specialist Projects
For this project, we use a modified version of a previously developed mathematical model, which describes the relationships among matrix metalloproteinases (MMPs), their tissue inhibitors (TIMPs), and extracellular matrix (ECM). Our ultimate goal is to quantify and understand differences in parameter estimates between patients in order to predict future responses and individualize treatment for each patient. By analyzing parameter confidence intervals and confidence and prediction intervals for the state variables, we develop a parameter space reduction algorithm that results in better future response predictions for each individual patient. Moreover, use of another subset selection method, namely Structured Covariance Analysis, that …
A Mathematical Model For Dengue Fever In A Virgin Environment, Jason K. Bowman
A Mathematical Model For Dengue Fever In A Virgin Environment, Jason K. Bowman
Senior Honors Projects
Dengue is a mosquito-borne viral infection found in tropical and subtropical regions around the world. The disease was named in 1779 and the first recorded epidemic of it occurred simultaneously on three continents within the following decade. Dengue is characterized by flu-like symptoms and, while its symptoms are generally reported as quite unpleasant, is rarely fatal. However, in some cases patients can contract a more serious form of the disease, known as Dengue Hemorrhagic Fever, which is far more dangerous. The World Health Organization estimates that today over 2.5 billion people are at risk for Dengue (over 40% of the …
Models Of Phototransduction In Rod Photoreceptors, Harihar Khanal, Vasilios Alexiades
Models Of Phototransduction In Rod Photoreceptors, Harihar Khanal, Vasilios Alexiades
Publications
Phototransduction is the process by which photons of light generate an electrical response in retinal rod and cone photoreceptors, thereby initiating vision. We compare the electrical response in salamander rods from increasingly more (spacialy) detailed models of phototransduction: 0-dimensional (bulk), 1-dimensional (longitudinal), 2-dimensional (axisymmetric), and 3-dimensional (with incisures). We discuss issues of finding physical parameters for simulation and validation of models, and also present some computational experiments for rods with geometry of mouse and human photoreceptors.
Optimal Therapy Regimens For Treatment-Resistant Mutations Of Hiv, Weiqing Gu, Helen Moore
Optimal Therapy Regimens For Treatment-Resistant Mutations Of Hiv, Weiqing Gu, Helen Moore
All HMC Faculty Publications and Research
In this paper, we use control theory to determine optimal treatment regimens for HIV patients, taking into account treatment-resistant mutations of the virus. We perform optimal control analysis on a model developed previously for the dynamics of HIV with strains of various resistance to treatment (Moore and Gu, 2005). This model incorporates three types of resistance to treatments: strains that are not responsive to protease inhibitors, strains not responsive to reverse transcriptase inhibitors, and strains not responsive to either of these treatments. We solve for the optimal treatment regimens analytically and numerically. We find parameter regimes for which optimal dosing …
A Mathematical Model For Treatment-Resistant Mutations Of Hiv, Helen Moore, Weiqing Gu
A Mathematical Model For Treatment-Resistant Mutations Of Hiv, Helen Moore, Weiqing Gu
All HMC Faculty Publications and Research
In this paper, we propose and analyze a mathematical model, in the form of a system of ordinary differential equations, governing mutated strains of human immunodeficiency virus (HIV) and their interactions with the immune system and treatments. Our model incorporates two types of resistant mutations: strains that are not responsive to protease inhibitors, and strains that are not responsive to reverse transcriptase inhibitors. It also includes strains that do not have either of these two types of resistance (wild-type virus) and strains that have both types. We perform our analysis by changing the system of ordinary differential equations (ODEs) to …