Ordinary Differential Equations and Applied Dynamics Commons^™

Differential Equation Modeling For Sustainable Resource Management: A Steady-State Optimal Harvesting Approach, Iordanka N. Panayotova, Aleksei Talonov

CODEE Journal

Mathematical models based on differential equations provide a powerful framework for connecting real-world data to informed decision-making. In this work, we present a student-accessible project that uses an optimal-control framework to study the sustainable management of biological resources.

Motivated by fisheries management, we examine a predator--prey system in which harvesting decisions must balance ecological and economic considerations. The model is formulated as an optimal control problem that seeks to maximize the total discounted net revenue from harvesting. Rather than solving for the complete time-dependent harvesting trajectory, we restrict the analysis to positive controlled coexistence equilibria and characterize an interior stationary …

Modeling Population Growth With Logistic And Modified Logistic Equations, Mihil Dimpal Patel

Discovery Day - Daytona Beach

Population growth models are essential tools for understanding how biological populations change over time under environmental constraints. This study examines population dynamics by comparing the classical exponential growth model with the logistic growth model. While exponential growth assumes unlimited resources and results in unbounded population increase, the logistic model incorporates a carrying capacity that limits growth as resources become scarce. To better represent real-world conditions, the logistic model is extended by introducing modifications such as harvesting terms and time-varying carrying capacities, which account for external removal of individuals and changing environmental limits. The equilibria of these models are determined, and …

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 …

Accuracy Of Parameter Estimation For A Simple Gene Regulatory Network Model Is Sensitive To Network Motif, Number Of Parameters Estimated, And Magnitude And Direction Of Regulatory Relationships, Nikki C. Chun, Kam Dahlquist

Honors Thesis

A gene regulatory network (GRN) is a set of transcription factors that regulate the expression of genes encoding other transcription factors. The dynamics of a GRN explain how gene expression changes over time. GRNmap is a MATLAB software package that uses ordinary differential equations to model dynamics of small-scale GRNs. We used the program to estimate production rates, expression thresholds, and regulatory weights for each transcription factor in three related literature-derived GRNs based on yeast cold shock microarray data previously collected in the Dahlquist Lab. We noticed large differences in estimated weight values when 1-2% of the expression values were …

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.

Gap Junction Architecture And Synchronization Clusters In The Thalamic Reticular Nuclei, Alex Norwood

Biology and Medicine Through Mathematics Conference

No abstract provided.

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.

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.

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.

Incorporating Thermal Performance Curves Into Population Dynamic Models For The West Nile Vector, Culex Pipiens, Benjamin Bruncati, Helle Aronson, Chloé Lahondère, Michael A. Robert

Biology and Medicine Through Mathematics Conference

No abstract provided.

Numerical Simulations And Hyers-Ulam Stability Of A Novel Nonlocal Anthropogenic Cutaneous Leishmaniasis Mathematical Model, Khalid Fanoukh Al Oweidi, Zakirullah -, Kamal Shah, Thabet Abdeljawad

Mathematical Modelling and Numerical Simulation with Applications

In this work, the fractal-fractional Atangana-Baleanu derivative with the Mittag-Leffler kernel is employed to capture the memory and hereditary effects inherent to anthropogenic cutaneous leishmaniasis transmission dynamics. The Banach fixed-point theorem and contraction mapping principle are used to prove the existence and uniqueness of solutions, while Hyers-Ulam stability of the system is analyzed to demonstrate the robustness of solutions with respect to small perturbations. Using a nonlinear least-squares approach, model parameters and fractional order are estimated using epidemiological data from the World Health Organization. The basic reproduction number $R_0 = 0.53$ indicates that the disease is under control after adding …

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 …

Construction And Data-Driven Analysis Of A Stochastic, Individual-Based Opioid Epidemiology Network Model, Leigh Bennett Pearcy, Owen Queen, Vincent Jodoin, Suzanne Lenhart, Christopher Strickland

Mathematical Modelling and Numerical Simulation with Applications

While substance use epidemiology has been an active area of mathematical research in recent years, the social and mental processes that are involved in the development of substance use disorders have presented challenges to advancing the epidemiological theory and how they differ from the contraction of pathogenic disease. Such distinction is especially pertinent in the context of the current United States opioid epidemic and its intersection with the recent COVID-19 pandemic, as both prescription drugs and social influence play major roles in the development of opioid use disorder. In this paper, we construct a stochastic network model capturing how individual …

(R2107) Analysis Of A Bivalent Vaccine Model With Peer Influence Effect On Testing, Manoj Kumar Singh, Anjali .

Applications and Applied Mathematics: An International Journal (AAM)

The coronavirus caused havoc around the world. There was a terrible situation in villages and cities, and no one knew how to deal with it. Although the governments of each country tried their best to save the common people, vaccination programs and testing centers were built everywhere. However, people were not utilizing it due to fear. Because of this, the infection spread rapidly. The qualitative study of the mathematical model here is in context with the situation when bivalent vaccination and testing are available for an epidemic. The mathematical model combines the exposed period and influenza model with vaccination included …

Data-Driven Modeling Of Dynamics And Adaptation In Mapk Pathway, Elisha Erzoah, Maria Emelianenko, Mariaelena Pierobon

Annual Symposium on Biomathematics and Ecology Education and Research

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.

[Kyda] The Behavioral Spillover Effect: Modeling Behavioral Interdependencies In Multi-Pathogen Dynamics, Leah Lejeune, Omar Saucedo, Lauren M. Childs, Navid Ghaffarzadegan

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Synaptic Dysfunction As Neural Contagion: A Graph-Based Sedr Framework For Simulating Signal Spread, Michelle Marfo, Dr. Padmanabhan Seshaiyer, Alonso Ogueda-Oliva

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Following Carbon: Pathway And Flux Representations Of Ecosystems, Caner Kazanci

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.

[Reev] Developing A Stage-Structure Stoichiometric Aquatic Tri-Trophic Food Chain Model, Ghislaine Niyodusenga, Cecilia Norris, Caroline Orza, Jing Li, Angela Peace, Greg Mayer, Rebecca A. Everett

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Analyzing The Effect Of A Holling Type Iii Functional Response On Predator-Prey Dynamics, Lawrence G. Seminario-Romero, Richard Rebarber, Brigitte Tenhumberg

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

[Lele] Early Careers In Mathematical Biology "Mathematical Analysis Of Exposure-Dependent Transmission With Environmental Reservoirs", Mohammad Mihrab Uddin Chowdhury, Angela Peace, Matthew J. Gray

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Metapopulation Model For Oyster Restoration, Leah Shaw

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

[Chu] Modelling The Effect Of Disturbed Blood-Feeding On Mosquito-Borne Disease Transmission, Kyle Dahlin, Michael Robert, Lauren Childs

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Understanding The Spread Of Black Sigatoka Disease: A Deterministic And Stochastic Modeling Approach, Bernard Asamoah Afful, Luis F. Gordillo

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Probiotic Bacterial Control Of White-Nose Syndrome In Little Brown Bat Colonies, Bethany Droubay, Alex Capaldi

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.