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
-
- Epidemiology (9)
- Medicine (8)
- Differential equations (3)
- HIV (2)
- Human immunodeficiency virus (2)
-
- Mathematical modeling (2)
- T cells (2)
- Treatment-resistant mutations (2)
- AIDS (1)
- Antiretroviral Therapy (1)
- Antiretroviral therapy (1)
- Biomathematics (1)
- COVID-19 (1)
- Cholera (1)
- Compartmental Models (1)
- Compartmental models (1)
- Continuous ODE model (1)
- Differential Equations (1)
- Differential equation model (1)
- Disease-free equilibrium (1)
- Dynamics (1)
- Ecology (1)
- Endemic equilibrium (1)
- Epidemic modeling (1)
- HIV Treatment (1)
- HIV infection (1)
- Hepatitis Action Plan (1)
- Hepatitis B vaccination (1)
- Immune System Dynamics Under HIV Infection (1)
- Infectious disease (1)
- Publication Year
- Publication
- Publication Type
Articles 1 - 30 of 66
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Modeling Fast Information And Slow(Er) Disease Spreading: A Geometric Analysis, Iulia Martina Bulai, Mattia Sensi, Sara Sottile
Modeling Fast Information And Slow(Er) Disease Spreading: A Geometric Analysis, Iulia Martina Bulai, Mattia Sensi, Sara Sottile
Biology and Medicine Through Mathematics Conference
No abstract provided.
Information Feedback Delays Within Epidemic Models And Their Effect On Model Dynamics., Maria K. Bouka, Christopher Strickland Dr
Information Feedback Delays Within Epidemic Models And Their Effect On Model Dynamics., Maria K. Bouka, Christopher Strickland Dr
Biology and Medicine Through Mathematics Conference
No abstract provided.
Modeling An Infection Outbreak With Quarantine: The Sibkr Model, Mikenna Dew, Amanda Langosch, Theadora Baker-Wallerstein
Modeling An Infection Outbreak With Quarantine: The Sibkr Model, Mikenna Dew, Amanda Langosch, Theadora Baker-Wallerstein
Rose-Hulman Undergraduate Mathematics Journal
Influenza is a respiratory infection that places a substantial burden in the world population each year. In this project, we study and interpret a data set from a flu outbreak in a British boarding school in 1978 with mathematical modeling. First, we propose a generalization of the SIR model based on the quarantine measure in place and establish the long-time behavior of the model. By analyzing the model mathematically, we determine the analytic formulas of the basic reproduction number, the long-time limit of solutions, and the maximum number of infection population. Moreover, we estimate the parameters of the model based …
A Tale Of Two Viruses: Why Smallpox Was Eradicated And Polio Persists, Katherine G. Mcgough, Erin N. Bodine
A Tale Of Two Viruses: Why Smallpox Was Eradicated And Polio Persists, Katherine G. Mcgough, Erin N. Bodine
Spora: A Journal of Biomathematics
The smallpox and poliomyelitis (polio) viruses were, at a time, one of the largest threats to global public health killing millions until global eradication campaigns were put into effect. Vaccination led to the eradication of smallpox and the elimination of polio for most of the world. However, polio continues to persist at endemic levels in Pakistan and Afghanistan. We developed ODE models of smallpox and polio to explore differences in transmission dynamics and determine if the underlying biology has made poliomyelitis more difficult to eradicate. Our model analysis shows there are multiple factors which should allow polio to have a …
Long-Acting Cabotegravir And The Emergence Of Drug-Resistant Hiv, Katharine Gurski
Long-Acting Cabotegravir And The Emergence Of Drug-Resistant Hiv, Katharine Gurski
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
An Ode Model For Investigating The Sleep-Pain Relationship In Sickle Cell Disease, Quindel Jones, Angela Reynolds, Rebecca Segal, Reginald Mcgee
An Ode Model For Investigating The Sleep-Pain Relationship In Sickle Cell Disease, Quindel Jones, Angela Reynolds, Rebecca Segal, Reginald Mcgee
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Physics-Informed Neural Networks For Agent-Based Epidemiological Model Calibration, Alvan C. Arulandu, Padmanabhan Seshaiyer
Physics-Informed Neural Networks For Agent-Based Epidemiological Model Calibration, Alvan C. Arulandu, Padmanabhan Seshaiyer
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Modeling Immune System Dynamics During Hiv Infection And Treatment With Differential Equations, Nicole Rychagov
Modeling Immune System Dynamics During Hiv Infection And Treatment With Differential Equations, Nicole Rychagov
CODEE Journal
An inquiry-based project that discusses immune system dynamics during HIV infection using differential equations is presented. The complex interactions between healthy T-cells, latently infected T-cells, actively infected T-cells, and the HIV virus are modeled using four nonlinear differential equations. The model is adapted to simulate long term HIV dynamics, including the AIDS state, and is used to simulate the long term effects of the traditional antiretroviral therapy (ART). The model is also used to test viral rebound over time of combined application of ART and a new drug that blocks the reactivation of the viral genome in the infected cells …
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 …
Physics-Informed Neural Networks For Informed Vaccine Distribution In Heterogeneously Mixed Populations, Alvan Arulandu, Padmanabhan Seshaiyer
Physics-Informed Neural Networks For Informed Vaccine Distribution In Heterogeneously Mixed Populations, Alvan Arulandu, Padmanabhan Seshaiyer
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Humanizing Mathematical Biology Research And Education, Carrie Diaz Eaton, Ognyan Simeonov
Humanizing Mathematical Biology Research And Education, Carrie Diaz Eaton, Ognyan Simeonov
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
The Effect Of Vaccine Misinformation On Disease Spread, Anthony Delegge, Yina Wang
The Effect Of Vaccine Misinformation On Disease Spread, Anthony Delegge, Yina Wang
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Stochastic Models Of Zoonotic Avian Influenza With Multiple Hosts, Environmental Transmission, And Migration In The Natural Reservoir, Kaia Smith
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
The Effect Of Prep Uptake And Adherence On The Spread Of Hiv In The Presence Of Casual And Long-Term Partnerships, Sylvia J. Gutowska, Katharine Gurski, Kathleen Hoffman
The Effect Of Prep Uptake And Adherence On The Spread Of Hiv In The Presence Of Casual And Long-Term Partnerships, Sylvia J. Gutowska, Katharine Gurski, Kathleen Hoffman
Biology and Medicine Through Mathematics Conference
No abstract provided.
Hepatitis B And D: A Forecast On Actions Needed To Reduce Incidence And Achieve Elimination, Scott Greenhalgh, Andrew Klug
Hepatitis B And D: A Forecast On Actions Needed To Reduce Incidence And Achieve Elimination, Scott Greenhalgh, Andrew Klug
Spora: A Journal of Biomathematics
Viral hepatitis negatively affects the health of millions, with the worst health outcomes associated with the hepatitis D virus (HDV). Fortunately, HDV is rare and requires prior infection with the hepatitis B virus (HBV) before it can establish infection and transmit. Here, we develop a mathematical model of HBV and HDV transmission in Sub-Saharan Africa to investigate the effects of hepatitis B vaccination on both HBV and HDV. Our findings illustrate a hepatitis B vaccination rate above 0.006 year-1 reduces hepatitis D by over 90%, and a vaccination rate above 0.0221 year-1 reduces hepatitis B by over 90%, …
Modeling, Analysis And Simulation Of Covid-19 Interaction Dynamics Between Local Community In Saudi Arabia And Visiting Sub-Population, Manal Badgaish, Padmanabhan Seshaiyer
Modeling, Analysis And Simulation Of Covid-19 Interaction Dynamics Between Local Community In Saudi Arabia And Visiting Sub-Population, Manal Badgaish, Padmanabhan Seshaiyer
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Mathematical Model For Understanding The Spread Of Covid-19 In Saudi Arabia With Access To Vaccination, Maha Alshabrawi
Mathematical Model For Understanding The Spread Of Covid-19 In Saudi Arabia With Access To Vaccination, Maha Alshabrawi
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Mathematical Modeling And Analysis Of Covid-19 Epidemic With Vaccination, Caitlin Seibel, Tina Huang, Jackson Reisman, Erika Johanna Martinez Salinas, Viswanathan Arunachalam, Moatlhodi Kgosimore, Anuj Mubayi, Padmanabhan Seshaiyer, Allen Bone Sehunelo
Mathematical Modeling And Analysis Of Covid-19 Epidemic With Vaccination, Caitlin Seibel, Tina Huang, Jackson Reisman, Erika Johanna Martinez Salinas, Viswanathan Arunachalam, Moatlhodi Kgosimore, Anuj Mubayi, Padmanabhan Seshaiyer, Allen Bone Sehunelo
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Mathematical Modeling, Analysis, And Simulation Of The Covid-19 Pandemic With Behavioral Patterns And Group Mixing, Comfort Ohajunwa, Padmanabhan Seshaiyer
Mathematical Modeling, Analysis, And Simulation Of The Covid-19 Pandemic With Behavioral Patterns And Group Mixing, Comfort Ohajunwa, Padmanabhan Seshaiyer
Spora: A Journal of Biomathematics
Due to the rise of COVID-19 cases, many mathematical models have been developed to study the disease dynamics of the virus. However, despite its role in the spread of COVID-19, many SEIR models neglect to account for human behavior. In this project, we develop a novel mathematical modeling framework for studying the impact of mixing patterns and social behavior on the spread of COVID-19. Specifically, we consider two groups, one exhibiting normal behavior who do not reduce their contacts and another exhibiting altered behavior who reduce their contacts by practicing non-pharmaceutical interventions such as social distancing and self-isolation. The dynamics …
Predicting Tumor Response To Radiotherapy Based On Estimation Of Non-Treatment Parameters, Yutian Huang, Allison L. Lewis
Predicting Tumor Response To Radiotherapy Based On Estimation Of Non-Treatment Parameters, Yutian Huang, Allison L. Lewis
Spora: A Journal of Biomathematics
Though clinicians can now collect detailed information about a variety of tumor characteristics as a tumor evolves, it remains difficult to predict the efficacy of a given treatment prior to administration. Additionally, the process of data collection may be invasive and expensive. Thus, the creation of a framework for predicting patient response to treatment using only information collected prior to the start of treatment could be invaluable. In this study, we employ ordinary differential equation models for tumor growth and utilize synthetic data from a cellular automaton model for calibration. We investigate which parameters have the most influence upon treatment …
Long-Term Dynamics Of The Kidney Disease Epidemic Among Hiv-Infected Individuals, Heather Gudaz, Henry A. Ogu, Elissa J. Schwartz
Long-Term Dynamics Of The Kidney Disease Epidemic Among Hiv-Infected Individuals, Heather Gudaz, Henry A. Ogu, Elissa J. Schwartz
Spora: A Journal of Biomathematics
One of many risks facing HIV+ individuals is the development of kidney dysfunction and end stage kidney disease (ESKD). A differential equation-based mathematical model was developed to assess the impact of antiretroviral therapy on the progression to kidney disease and on reducing mortality due to kidney failure. Analytical and numerical predictions of long-term HIV+ ESKD prevalence show that therapy can lead to either extremely low levels of disease prevalence or increased prevalence, depending on drug efficacy levels and mechanisms of action. Maintenance of HIV+ ESKD prevalence below one individual is possible with sufficient efficacy (e.g., 99%) against the progression from …
Applying Immuno-Epidemiology Principles To Violence, Anna H. Sisk, Nina H. Fefferman, Judy Day, Patricia Bamwine
Applying Immuno-Epidemiology Principles To Violence, Anna H. Sisk, Nina H. Fefferman, Judy Day, Patricia Bamwine
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Analyzing The Control Measures For The Homeless Population And Quantifying Their Impact On The Covid-19 Epidemic In New York City, Steven Manns
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Mathematical Modeling And Analysis Of The Zika Virus Epidemic With Human Mobility And Parameter Estimation For Localities In Puerto Rico, Carmen Caiseda
Mathematical Modeling And Analysis Of The Zika Virus Epidemic With Human Mobility And Parameter Estimation For Localities In Puerto Rico, Carmen Caiseda
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
A Teaching Module For Mathematical Epidemiology Using Matlab Or R, Glenn Ledder
A Teaching Module For Mathematical Epidemiology Using Matlab Or R, Glenn Ledder
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Assess The Impacts Of Human Mobility Change On Covid-19 Using Differential Equations With Google Community Mobility Data, Nao Yamamoto
Assess The Impacts Of Human Mobility Change On Covid-19 Using Differential Equations With Google Community Mobility Data, Nao Yamamoto
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Mathematical Modeling, Analysis, And Simulation Of The Covid-19 Pandemic With Behavioral Patterns, Risk Perception, And Group Mixing, Comfort Ohajunwa, Padmanabhan Seshaiyer
Mathematical Modeling, Analysis, And Simulation Of The Covid-19 Pandemic With Behavioral Patterns, Risk Perception, And Group Mixing, Comfort Ohajunwa, Padmanabhan Seshaiyer
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
In Silico Modelling For The Treatment Of Gastric Cancer, Leonardo F. Martinez, Diana Gamboa, Paul A. Valle
In Silico Modelling For The Treatment Of Gastric Cancer, Leonardo F. Martinez, Diana Gamboa, Paul A. Valle
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Mathematical Modelling And In Silico Experimentation To Estimate The Quantity Of Covid-19 Infected Individuals In Tijuana, México, Karla A. Encinas, Luis N. Coria, Paul A. Valle
Mathematical Modelling And In Silico Experimentation To Estimate The Quantity Of Covid-19 Infected Individuals In Tijuana, México, Karla A. Encinas, Luis N. Coria, Paul A. Valle
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Using Network Modeling To Understand The Relationship Between Sars-Cov-1 And Sars-Cov-2, Elizabeth Brooke Haywood, Nicole A. Bruce
Using Network Modeling To Understand The Relationship Between Sars-Cov-1 And Sars-Cov-2, Elizabeth Brooke Haywood, Nicole A. Bruce
Biology and Medicine Through Mathematics Conference
No abstract provided.