Ordinary Differential Equations and Applied Dynamics Commons^™

Numerical Analysis Of The Sir Model For Predicting Disease Spread, Victoria Gaibor, Isabel Tejada, Kate Moore

Discovery Day - Daytona Beach

This project, Numerical Solutions of the SIR Model for Predicting Disease Spread, investigates the application of numerical methods to analyze the dynamics of infectious diseases using the classical Susceptible–Infected–Recovered (SIR) model. The SIR model, a system of nonlinear ordinary differential equations, is widely used to describe how diseases such as COVID-19 propagate through a population. The primary objective of this study is to solve the SIR initial value problem using multiple numerical techniques, including Euler’s method, Runge–Kutta methods, and multistep methods, and to compare their accuracy and efficiency. The model is implemented using given initial conditions and parameters, and additional …

Simulating Pacemakers And Heartbeat Recovery Through Mathematical Modeling, Thomas Estrada, Jayla Edwards

Discovery Day - Daytona Beach

Title: Simulating Pacemakers and Heartbeat Recovery Through Mathematical Modeling   This study utilizes the Fitzhugh-Nagumo model to simulate cardiac electrical activity and the regulatory role of pacemakers through ordinary differential equations (ODEs). By defining the rate of change for membrane voltage, 𝑑𝑣/dt, and a recovery variable, 𝑑𝑤/dt, the model captures the heart's excitability and resting states. Central to the analysis is the stimulus current parameter, which represents the "kick" provided by a pacemaker to correct flatline conditions or weak heartbeats. Using Euler’s method for numerical integration, the research compares unstable cardiac rhythms against corrected periodic oscillations. Additionally, the project implements vector …

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

Spora: A Journal of Biomathematics

In response to a significant tuberculosis outbreak in Wyandotte and Johnson Counties, Kansas, this study presents a compartmental model of ordinary differential equations to evaluate the impact of standard antibiotic treatment. The model incorporates latent, active, and treated disease states. Parameter values were informed by epidemiological data and uncertain parameter value ranges were explored systematically through uncertainty analysis using constrained Latin hypercube sampling. Cumulative infections and deaths, and the basic reproduction number, were computed over a five-year simulation period. Sensitivity analyses using partial rank correlation coefficients identified symptomatic treatment rate and transmission rate as primary drivers of cumulative infections and …

Dynamic Homeostasis In Relaxation And Bursting Oscillations, Christopher J. Ryzowicz

Biology and Medicine Through Mathematics Conference

No abstract provided.

Modeling The Effects Of Chronic Stress On Type 2 Diabetes, Kris Mae Pasia

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Mechanistic Model Of Adhesion, Inflammation, Sleep, And Pain In Sickle Cell Patients, Milan Marsh, Rebecca Segal

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Logic-Based Differential Equation Model Of Endothelial Cell Function, Ella Froedge, Scarlett Hamilton, Mitchel Colebank

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Phylogeny Informed Mathematical Model Of Hpai H5n1 Transmission And Control In Multi Host Systems, Oluwatosin Babasola

Biology and Medicine Through Mathematics Conference

No abstract provided.

Mathematical Modeling Of The Combined Effects Of Thermal Burn And Local Irradiation, Quintessa Hay, Rachel Jennings, Amy Creel, Kyle Gaffney, Christina Wagner, Kidist Maxwell, Ginu Unnikrishnan, Tyler Dant

Biology and Medicine Through Mathematics Conference

No abstract provided.

Mitigating Parameter Identifiability Issues Through Model Calibration On The Data-Informed Active Subspace: An Example In Tumor Growth, Allison L. Lewis, Rebecca A. Everett

Biology and Medicine Through Mathematics Conference

No abstract provided.

Stochastic Universal Differential Equations For Epidemiological Modeling: Uncertainty Quantification In Disease Transmission Dynamics, Alice Menaya Armah-Bonney

Electronic Theses and Dissertations

Epidemic forecasting requires not only predictions of expected case counts, but also quantification of uncertainty, although existing surrogate modeling frameworks for agent-based models remain fundamentally deterministic. In this thesis a Stochastic Universal Differential Equation framework is presented that extends the deterministic Universal Differential Equation approach by incorporating a learnable stochastic diffusion term, enabling calibrated probabilistic forecasts while preserving the mechanistic interpretability and computational efficiency of the deterministic baseline. In doing so, a two-phase training algorithm is introduced to ensure stable convergence and the framework is validated against the ensemble output from ExaEpi, an exascale agent-based model of a COVID-19 outbreak …

Managing Multi-Drug Resistance: An Evolutionary Game Theory And Optimal Control Approach, Shukhrat Nasrulloev

Theses and Dissertations

Multi-drug resistance is an evolutionary process in which treatment eliminates sensitive cells, allowing resistant clones to dominate. This thesis investigates this process using a framework integrating population dynamics, evolutionary game theory, and optimal control theory. We develop a two-population logistic growth model describing competition between drug-sensitive and drug-resistant cells under treatment, construct dose-dependent payoff matrices and replicator dynamics to characterize evolutionary competition, and derive a critical drug level D_crit = (r_S - rR)/(dS - d_R) at which resistant cells gain a fitness advantage. An optimal control problem is formulated via Pontryagin's Maximum Principle to identify schedules …

A Novel Mathematical Model Of Hiv Transmission Incorporating The Effects Of Treatment And Pre-Exposure Prophylaxis: Sensitivity Analysis And Numerical Simulations, Erick Manuel Delgado Moya

Mathematical Modelling and Numerical Simulation with Applications

Human immunodeficiency virus (HIV) continues to be a public health problem in many countries of the world, and Pre-exposure prophylaxis (PrEP) is a preventive method for HIV, which has shown great efficacy and is in use worldwide. This work presents a new mathematical model for HIV transmission incorporating PrEP use and evaluates the impact of PrEP along with its increasing use in a population. The construction of the model takes into account three forms of diagnosis: diagnosis of individuals in risky sexual contact, diagnosis after risky contact (diagnosis in the undiagnosed infected compartment), and diagnosis associated with attempting to enter …

Multi-Resolution Graph Neural Networks For Spread Prediction, Petr Kisselev

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Metapopulation Model To Evaluate C.Difficile Potential Vaccine Interventions., Archana Neupane Timsina

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Novel Mathematical Model Of Oropouche Virus Transmission Dynamics, Darsh Gandhi, Carli Peterson, Emma Slack, Elizabeth Rubio, Amira Claxton, Christopher M. Kribs

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

[Lele] Measles And Mandates– What Will Happen If Florida Repeals The Mmr Vaccine Mandate?, Alice Oveson, Abba Gumel

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Parameter Estimation And Simulation In Pollution-Induced Asthma Disease Model Using Physics-Informed Neural Networks, Aadi Gannavaram

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Sickle Cell Disease Using A Sleep-Pain-Inflammation Cycle, Milan Marsh

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling, Analysis, And Prediction Of Covid-19 Dynamics With Interacting Subpopulations And Implicit Behavior Using Physics-Informed Neural Networks, Naima Aubry-Romero, Alonso Ogueda-Oliva, Padmanabhan Seshaiyer

Spora: A Journal of Biomathematics

In this paper, we consider an extended SEIR compartmental model that incorporates young and old interacting subpopulations, allowing for cross-group transmission dynamics. Implicit behavioral changes are included to determine the influence of social behavior on coronavirus transmission dynamics. The basic reproduction number, the average number of secondary cases of infection produced by a single primary case, is derived for both the explicit and implicit model using the next-generation matrix method. We solve the associated differential equation systems and estimate useful parameters in the explicit model using physics-informed neural networks (PINNs). Our results point to how the PINNs approach offers an …

Quantitative Preventive Approaches To Diabetes: Mathematical Modeling And Analysis, Rushi P. Bhatt

Theses, Dissertations and Culminating Projects

The rising prevalence of diabetes presents a pressing global health concern, necessitating effective control strategies. This study aims to construct a mathematical model to analyze the influence of diverse factors on blood sugar levels, with a focus on identifying optimal methods for maintaining healthy glucose levels. Employing ordinary differential equations (ODE), the model investigates variables including leptin resistance, fat mass, glucose, insulin resistance, beta cell mass, daily physical activity, and dietary intake. Utilizing parameter estimates from existing literature, the model’s framework is established, and simulation results elucidate the intricate interplay between lifestyle choices and blood glucose dynamics. Furthermore, the model …

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 …

Leveraging Quantitative Systems Pharmacology For Dose Optimization In Oncology Drug Development, Blerta Shtylla

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Kreig: Gaining Insight Into Epidemics Through Use Of Mathematical Modeling, Christina Edholm

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Improving Infectious Disease Predictions Through The Use Of Metapopulation Sir Modeling And Graph Convolutional Neural Networks, Petr Kisselev, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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.

Modeling And Control Of Drug Resistance In Cancer Dynamics, James Greene

Biology and Medicine Through Mathematics Conference

No abstract provided.

Using Splines To Investigate The Effects Of Temperature On The Within-Mosquito Malaria Parasite Forms, Alexander J. Diefes, Miranda I. Teboh-Ewungkem

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

Biology and Medicine Through Mathematics Conference

No abstract provided.

Proof-Of-Concept For Converging Beam Small Animal Irradiator, Benjamin Insley

Dissertations and Theses (Open Access)

The Monte Carlo particle simulator TOPAS, the multiphysics solver COMSOL., and

several analytical radiation transport methods were employed to perform an in-depth proof-ofconcept

for a high dose rate, high precision converging beam small animal irradiation platform.

In the first aim of this work, a novel carbon nanotube-based compact X-ray tube optimized for

high output and high directionality was designed and characterized. In the second aim, an

optimization algorithm was developed to customize a collimator geometry for this unique Xray

source to simultaneously maximize the irradiator’s intensity and precision. Then, a full

converging beam irradiator apparatus was fit with a multitude …