Ordinary Differential Equations and Applied Dynamics Commons^™

Dynamical Behavior, Extinction And Persistence In A Stochastic Delayed Two-Strain Epidemic Model With A Generalized Crowley-Martin Incidence Rate, Amina Allali, Dounia Bentaleb, Saida Amine

Mathematical Modelling and Numerical Simulation with Applications

This paper develops and analyzes a novel delayed stochastic SIR epidemic model with two interacting strains and general incidence functions. By establishing the existence and uniqueness of a positive global solution, the well-posedness of the model under stochastic perturbations is ensured. Extinction occurs when the stochastic reproduction number falls below unity, as demonstrated through Itô calculus and martingale convergence theorems, while persistence is guaranteed under the Crowley–Martin incidence when it exceeds one. Numerical experiments based on the Positive Preserving Truncated Euler–Maruyama (PPTEM) scheme confirm the analytical predictions and highlight the influence of time delay and noise intensity on the long-term …

Dynamical Systems Modeling To Determine The Role Of Crosstalk In Shaping Stat Signaling Profiles, Laura F. Strube, Anamarie Martinez, Neha Cheemalavagu, Karsen Shoger, James Faeder, Rachel Gottschalk

Biology and Medicine Through Mathematics Conference

No abstract provided.

[Kyda] Biologically Grounded Surrogate-Driven Parameter Inference For Sparsely Observed Dynamical Systems, Joshua C. Macdonald

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Immune Dysregulation In Covid-19: Mathematical Modeling Of The Within-Host Dynamics, Pagnapech Ngoun, Nicolas Alvarez, Ayesh Awad, Hwayeon Ryu

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling The Impact Of Treatment During An Ongoing Tuberculosis Outbreak, Bach Le, Jude Shive, Erin N. Bodine

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Stability Insights From Modeling Chronic Myelogenous Leukemia, Giovani Thai

Master's Theses

This thesis centers around a model for chronic myelogenous leukemia (CML) as it behaves under imatinib treatment, a common medication for CML patients, and the anti-leukemia immune response. The dynamics are represented with a system of nonlinear delay-differential equations first constructed by Kim et al. in 2008, capturing population changes of T-cells and various CML growth stages. We investigate stability in both the clinical and mathematical sense. Through numerical simulations, we computationally incorporate a supplementary treatment plan to determine its effectiveness in aiding immune response and medication in achieving remission and full elimination. The primary goal is to conduct a …

Mathematical Modelling Of Disease Outbreak, Favour Christian, Matthew Molloy

SURE Journal: Science Undergraduate Research Experience Journal

Establishing a model framework for more research necessitates a thorough understanding of the causes, distribution, prevalence, and evolution of infectious illnesses. The main mathematical concept used in this modelling simulation is ordinary differential equations (ODEs). The purpose of this study was to investigate the significance of the many criteria linked to a zombie virus spread. The zombie framework provides an accessible and relatively simple representation of the nature of infectious disease spread, allowing for tractable assumptions and the development of more complex situations.

The models are designed around a zombie outbreak in which the zombie virus is spread through a …

Incorporating Adaptive Human Behavior Into Epidemiological Models Using Equation Learning, Austin Barton, Jordan Klein, Jonathan Greer, Kevin Flores, Patrick Haughey

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Mathematical Model Of Acanthocephalan Parasite Infection In Gull-Billed Terns, Charlotte Moser

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling The Immune Response To Immunotherapy And Triple Negative Breast Cancer In Mice, Dayton J. Syme, Angelica Davenport, Yun Lu, Anna G. Sorace, Nicholas G. Cogan

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Dynamical System Model Of Dengue Transmission For Rio De Janeiro, Brazil, Gregory Schmidt, Benjamin Whipple, Vinodh Chellamuthu, Xiaoxia Xie

Spora: A Journal of Biomathematics

The dengue virus is a serious concern in many parts of the world, including Brazil. As data indicates, a prominent vector for dengue is the mosquito Aedes aegypti. By using the dengue incidence records from the Brazilian SINAN database, we estimate the population of A. aegypti within the city of Rio de Janeiro. Using historical climate data for Rio de Janeiro and the computed population estimates, we extend an existing model for the population dynamics of mosquitoes to incorporate precipitation in aquatic stages of development for A. aegypti.

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 …

Mathematical Model Of Immune-Inflammatory Response In Covid-19 Patients, Quiyana M. Murphy

Biology and Medicine Through Mathematics Conference

No abstract provided.

Flattening The Curve: The Effects Of Intervention Strategies During Covid-19, Kelly A. Reagan, Rachel J. Pryor, Gonzalo M. Bearman, David M. Chan

Spora: A Journal of Biomathematics

COVID-19 has plagued countries worldwide due to its infectious nature. Social distancing and the use of personal protective equipment (PPE) are two main strategies employed to prevent its spread. A SIR model with a time-dependent transmission rate is implemented to examine the effect of social distancing and PPE use in hospitals. These strategies’ effect on the size and timing of the peak number of infectious individuals are examined as well as the total number of individuals infected by the epidemic. The effect on the epidemic of when social distancing is relaxed is also examined. Overall, social distancing was shown to …

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

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Effect Of Fcgammariia Polymorphisms On Dengue Outbreak Severity, Leah Darwin, Richard V. Clarke

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling And Preparedness: The Transmission Dynamics Of Covid-19 Outbreak In Provinces Of Ecuador, Carlos E. Bustamante Orellana, Jordy Cevallos-Chavez, Cesar Montalvo, Jeff Sulliavan, Edwin Michael, Anuj Mubayi

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

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modeling Of The Car T-Cell Therapy, Emek Kose, Elizabeth Zollinger, Samantha Elliott

Biology and Medicine Through Mathematics Conference

No abstract provided.

Combating Tuberculosis: Using Time-Dependent Sensitivity Analysis To Develop Strategies For Treatment And Prevention, Kendall B. Clark, Mayleen Cortez, Cristian Hernandez, Beth E. Thomas, Allison L. Lewis

Spora: A Journal of Biomathematics

Although many organizations throughout the world have worked tirelessly to control tuberculosis (TB) epidemics, no country has yet been able to eradicate the disease completely. We present two compartmental models representing the spread of a TB epidemic through a population. The first is a general TB model; the second is an adaptation for regions in which HIV is prevalent, accounting for the effects of TB/HIV co-infection. Using active subspaces, we conduct time-dependent sensitivity analysis on both models to explore the significance of certain parameters with respect to the spread of TB. We use the results of this sensitivity analysis to …

Understanding The Role Of Macrophages In Lung Inflammation Through Mathematical Modeling, Sarah B. Minucci

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Mathematical Model Of The Inflammatory Response To Pathogen Challenge, Lester Caudill, Fiona Lynch

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling The Transmission Of Wolbachia In Mosquitoes For Controlling Mosquito-Borne Diseases, Zhuolin Qu

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Parameter Sensitivity For In Vitro Anthrax Studies, Yareley Gonzalez, Maria Macias-Bedolla, Megan O. Powell

Spora: A Journal of Biomathematics

Studies done on interactions between spores and macrophages done in vitro show inconsistent results based on experimental protocol and inhibit meaningful extrapolation to in vivo. In this study, we perform a sensitivity analysis of a model representing in vitro studies of interactions between anthrax spores and macrophages to help address the effects of these inconsistencies. We perform both local and global analyses using Latin hypercube sampling and partial rank correlation coefficients. Our analysis indicates the amount of intracellular bacteria over time is most sensitive to the killing of intracellular bacteria by the macrophages and replication of the bacteria inside …

Quantifying Effects Of Neutrophil Memory On Migration Patterns Using Microfluidic Platforms And Ode Modeling Of The Mechanistic Molecular Pathways, Brittany P. Boribong, Mark J. Lenzi, Mirjam Sarah Kadelka, Stanca Ciupe, Liwu Li, Caroline N. Jonea

Biology and Medicine Through Mathematics Conference

No abstract provided.

Age-Structured And Vaccination Models Of Devil Facial Tumor Disease, Christopher D. Bruno, Timothy Comar, Megan O. Powell, Adjo Tameklo

Spora: A Journal of Biomathematics

Tasmanian devil populations have been devastated by devil facial tumor disease (DFTD) since its first appearance in 1996. The average lifespan of a devil has decreased from six years to three years. We present an age-structured model to represent how the disease has affected the age and breeding structures of the population. We show that with the recent increase in the breeding of juvenile devils, the overall devil population will increase but not nearly to pre-DFTD levels. The basic reproductive number may be increased with the influx of young breeding devils. In addition, our model shows that the release of …

The Kinetics Of Type I Interferons During Influenza A Virus Infection, Margaret A. Myers

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Model Of Dengue Transmission With Wolbachia-Free And Wolbachia-Infected Mosquitoes, Iftikhar Ahmed

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Role Of Intermittent Preventive Treatment For Malaria In Saving Lives And Promoting Drug Resistance, Carrie Manore

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.