Applied Mathematics Commons^™

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.

Balancing Stability And Complexity In Boolean Models Of Biological Networks, Venkata Sai Narayana Bavisetty

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Compartmental Model For Periodic Animal Migration, Rhianna Yates, Leah Glasser, Elena Wheatley, Christopher Hay-Jahans

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Spatial Strategies In Ants: Modeling Polydomy, Saya Zeleznik, Fred Adler

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Optimizing The Distribution Of Fruiting Agave On Bat-Friendly Tequila Plantations, Grace Gorreck, Clarissa Azurin, Lois Carpenter

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Paclobutrazol Enhances Tall Fescue Salt Tolerance Via Physiological And Root System Architecture Modulation, Shugao Fan, Xindi Sun, Guohao Liang, Zhuanzhuan Ma, Jincheng Hao, Jiawei Wu, Ying Zhao

School of Mathematical & Statistical Sciences Faculty Publications

Background: Salinity represents a major global constraint on crop productivity. Promoting the cultivation of tall fescue in saline environments offers not only nutritional advantages for livestock but also enhances its potential for ornamental use. In this mesocosm study, we examined the effects of paclobutrazol (PBZ) on tall fescue performance under salt stress, focusing on key physiological traits to evaluate salt tolerance.

Results: Under high salt stress, paclobutrazol application increased the total number of lateral roots by 85%, from 18.39 to 34.04, and widened their growth angle by 24%, from 24.10° to 29.88°, fundamentally enhancing topsoil exploration. This reconfigured root system …

(Si15-107) Mathematical Modeling Of Cancer Dynamics Stability Analysis Of Post Therapy Protection, Rajendran Swetha, Tharmalingam Gunasekar, Kamalendra Kumar, Krishnasamy Sakthivel

Applications and Applied Mathematics: An International Journal (AAM)

The study of PSITPS mathematical model is developed to analyze cancer dynamics, focusing on post-therapy protection. The model’s solution is rigorously examined for boundedness and positivity of solutions. Equilibrium points are identified, and numerical methods are employed to study stability. Simulations using accurate cancer data demonstrate the effectiveness of post-treatment protection in controlling cancer spread and minimizing recurrence. Stability analysis confirms the model’s predictive capability, offering valuable insights into long-term patient outcomes. The results highlight the importance of continuous post-treatment care in improving survival rates and reducing disease prevalence. This study provides a framework for optimizing cancer treatment strategies by …

(Si15-121) Analyzing Seitr Tuberculosis Transmission Model Using Caputo–Fabrizio Fractional Derivative With Diverse Contact Rates, S. S. Sumaiya Banu, T. Gunasekar, S. Manikandan, Kamalendra Kumar, M. Suba

Applications and Applied Mathematics: An International Journal (AAM)

In the modern age, tuberculosis remains a pressing global health concern. Our study introduces and evaluates the SEITR pandemic TB transmission model, dividing the population into five compartments to explore distinct characteristics relevant to our investigation. Additionally, we delve into the application of fractional calculus. Through the Laplace transform method, we derive series solutions for all compartments, ensuring their existence and uniqueness. We also investigate the reproduction number of the tuberculosis epidemic model, examining how varying contact rates impact disease spread. We apply the predictor-corrector method for the Caputo-Fabrizio fractional derivative to verify the accuracy of our approach. This accurately …

Dynamics And Optimal Intervention Strategies In A Shigellosis Transmission Model, Mehmet Gümüs, Shewafera Wondimagegnhu Teklu, Kemal Türk

Mathematical Modelling and Numerical Simulation with Applications

This research explores how water treatment contributes to limiting the transmission of Shigellosis, an infection caused by bacteria from the Shigella genus. A mathematical framework is formulated to evaluate the influence of protective strategies and water purification on the spread of the disease. To confirm the model's biological relevance, its well-posedness is investigated. The basic reproduction number $(\mathfrak{R}_0)$, a critical indicator of disease behavior, is derived using the matrix operator method. Findings indicate that if $\mathfrak{R}_01$, the infection persists, with the endemic equilibrium exhibiting local asymptotic stability. A comprehensive cost-effectiveness analysis reveals that combining environmental protection with water treatment represents …

Investigating Potential Alzheimer's Disease Therapies Through An Agent-Based Model Of Impaired Microglia Metabolismmodeling Impaired Microglia Metabolism, Cheyenne Ty, Abigail Penland, John Gerving, Martin Mendoza-Ceja, Megan Pratt, Kamila Larripa

Spora: A Journal of Biomathematics

Alzheimer’s disease is the leading cause of dementia globally and is marked by amyloid-β plaque accumulation, decreased brain pH, disrupted metabolism, and increased permeability of the blood-brain barrier. Microglia, the resident immune cells of the central nervous system, are essential for maintaining brain homeostasis and are critically involved in the progression of AD. While microglia can initiate protective immune responses to injury and disease, dysregulated microglial metabolism may contribute to the exacerbation of Alzheimer's pathology. To investigate potential therapeutic strategies, we developed an agent-based model simulating the effects of exercise and metabolic enhancement on dysfunctional microglia. Our findings suggest that …

Coarse-Graining Spiking Reservoirs: Reducing Reservoir Size While Preserving Critical Dynamics, Tucker X. Mastin, Christof Teuscher

Northeast Journal of Complex Systems (NEJCS)

We propose an extension of renormalization into the domain of spiking neural networks, thereby providing a novel framework for coarse-graining neural networks without disrupting their critical properties. The proposed coarse-graining technique merges neurons and synaptic connections based on a graph-theoretic distance derived from synaptic weight strength and is configured to effectively prune the reservoir size while preserving the scale-free spiking dynamics indicative of criticality. Criticality in spiking neural networks may provide information-theoretic advantages by optimizing information processing and sensitivity to input. Using time-series prediction benchmarks, we demonstrate that networks operating at criticality exhibit up to 32% higher prediction accuracy before …

Evolutionary Dynamics Of Artificial Agents: Exploration And Learning In Games, Brian Mintz

Dartmouth College Ph.D Dissertations

The natural world abounds with examples of complex behavior in humans and many other species. Evolutionary game theory is a powerful mathematical framework to understand the origins of many such behaviors like cooperation. Since these behaviors are often selected against initially, understanding why they are so widespread has been a longstanding question. Rather than assuming agents' rationality, like in traditional game theory, this approach studies the mutation and selection of strategies themselves. However most behavior is neither perfectly rational nor entirely determined by genetics. This dissertation works to bridge the gap between these two perspectives by analyzing models where individuals …

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 …

Sliding Window Method For Simulating Action Potentials In Axons, Hayden Reed

Honors Theses

ABSTRACT Hodgkin and Huxley’s nonlinear partial differential equations model the excitation and propagation of action potentials in neurons, and there have been numerous attempts at finding the best numerical solution method. This thesis proposes a novel approach to solving these equations: the Sliding Window method, in which a fixed sub-interval is found through capturing the signal’s head and tail. The system is then solved on the sub-interval instead of the entire interval. Using the Sliding Window technique also involves implementing the backward and forward Euler methods and the finite difference method. It will be demonstrated that, in utilizing the Sliding …

Evaluating Risk And Return Of Corn And Soybean Marketing Strategies Using Monte Carlo Simulation Methods, Johanna Ilves

Department of Agricultural Economics: Dissertations, Theses, and Student Research

This study evaluates the performance of pre-harvest marketing strategies for corn and soybeans, using Monte Carlo simulation techniques. Given the increasing volatility in commodity prices and the evolving landscape of agricultural markets, producers face growing challenges in developing effective marketing plans that manage risk and enhance profitability. This thesis examines thirteen marketing strategies from 2008 to 2024, including benchmark harvest-only sales and various pre-harvest futures contract approaches. Historical futures price data for December corn and November soybean contracts were used to simulate 1,000 marketing outcomes per strategy per year, capturing a broad range of market conditions. Key performance indicators such …

Identifying And Characterizing Transition Cells In Developmental Processes From Scrna-Seq Data, Yuanxin Wang

Dissertations and Theses (Open Access)

During the development of multicellular organisms, individual cells make distinct decisions about their cell types and states. Understanding the molecular mechanisms underlying cellular state transitions at different developmental stages provides deep insights into physiology, morphology and the etiology of diseases. Single-cell RNA-sequencing (scRNA-seq), which is widely used to study complex cell states and dynamic gene expression patterns, enables us to investigate molecular mechanisms of cellular state transitions. Currently, however, computational tools available for identifying cellular states and state transitions remain limited.

Although trajectory-based methods such as Monocle and Slingshot assume that state transitions generate continuous expression profiles, they cannot distinguish …

Developing An Unfolding-Incorporated Coarse-Grained Polymer Model For Fibrinogen To Study The Mechanical Behaviour, Vivek Sharma, Poulomi Sadhukhan

Northeast Journal of Complex Systems (NEJCS)

Fibrinogen is a protein found in blood that forms Fibrin polymer network to build a clot during wound healing process when there is a cut in the blood vessel. The fibrin fiber is highly stretchable and shows a complex mechanical properties. The fibrin monomer, Fibrinogen, has a very complex structure which is responsible for its unusual elastic behaviour. In this work, we focus on mechanism of unfolding of D-domain of Fibrinogen, and study its effect in the mechanical behaviour. We develop a coarse-grained (CG) bead-spring model for Fibrinogen which captures the unfolding of folded D-domains along with other necessary structural …

Using Mathematical Modeling To Study The Dynamics Of Legionnaires’ Disease And Consider Management Options, Mark Z. Wang, Christina J. Edholm, Lihong Zhao

Faculty Articles

Legionnaires' disease (LD) is a largely understudied and underreported pneumonic environmentally transmitted disease caused by the bacteria \textit{Legionella}. It primarily occurs in places with poorly maintained artificial sources of water. There is currently a lack of mathematical models on the dynamics of LD. In this paper, we formulate a novel ordinary differential equation-based susceptible-exposed-infected-recovered (SEIR) model for LD. One issue with LD is the difficulty in its detection, as the majority of countries around the world lack the proper surveillance and diagnosis methods. Thus, there is not much publicly available data or literature on LD. We use parameter estimation for …

An Agent-Based Model Of Microglia And Neuron Interaction: Implications In Neurodegenerative Disease, Cheyenne Ty, Amanda Case, Emmanuel Mezzulo, Abigail Penland, Kamila Larripa

Spora: A Journal of Biomathematics

Whether immune cells protect or harm the brain is an open question depending on context, and their role is implicated in multiple diseases such as Alzheimer's disease, dementia, and other neurological disorders. Microglia, a specific type of immune cell in the central nervous system, play a key role in homeostasis, and genes associated with an elevated risk of Alzheimer's disease correspond with deficiencies in their behavior. We created an agent-based model that incorporates inflammatory signaling, chemotaxis, and phagocytosis of damaged neurons and allows the exploration of crucial pathways in the maintenance of brain health. We specifically investigated pathways related to …

On Solving Differential Equations Describing The Ecology Of Shallow Lakes: A Comparison Of Classical And Modern Computational Methods Through Python, Vruddhi Kapre, Jeffrey R. Anderson, Alessandro Maria Selvitella

Spora: A Journal of Biomathematics

In this exposition paper, we describe some computational methodologies to solve numerically differential equations modeling the shallow lake ecosystem, with particular focus on the dynamics of the phosphorus. We describe in detail Python implementations of classical algorithms, like Runge-Kutta, and more modern approaches, including physics-informed neural networks.

Optimizing Decision-Making In A Cerebral Palsy Model Using Reinforcement Learning, Richard Ampah

Pitzer Senior Theses

This study presents an original interdisciplinary investigation into how reinforcement learning (RL) can model motor and cognitive defects and potentially improve motor and cognitive functions in individuals with cerebral palsy (CP), a non-progressive neurological disorder that impairs movement and adaptability. Integrating computational neuroscience and machine learning, the research applies policy gradient methods and Markov Decision Processes (MDPs) to simulate adaptive learning in agents with and without CP-related constraints.

The central aim is to compare the cumulative rewards of optimal policies, derived from value iteration, and human-like learning policies using the REINFORCE algorithm, both with and without the Bellman baseline. The …

Geometric Modeling, Reconstruction And Evaluation Of Maize Leaf Morphology In 3d, Zhaocheng Xiang

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

Maize is a vital crop for global food security, yet quantitative characterization of its three-dimensional (3D) morphology remains a major challenge due to the geometric complexity of curved leaf structures and occlusions during data collection. This work presents an integrated framework for the digital reconstruction, parametric modeling, and functional analysis of maize leaf morphology and canopy architecture, advancing the precision and interpretability of phenotyping and modeling in smart agriculture.

First, we propose a descriptive and parametric model that represents maize leaves through three fundamental components: midrib, cross-section, and blade contour. Each is described by geometric curves and controlled by biologically …

Covariate Selection For Rna-Seq Differential Expression Analysis With Hidden Factor Adjustment, Farzana Noorzahan, Hyeongseon Jeon, Yet Nguyen

Mathematics & Statistics Faculty Publications

In RNA-seq data analysis, a primary objective is the identification of differentially expressed genes, which are genes that exhibit varying expression levels across different conditions of interest. It is widely known that hidden factors, such as batch effects, can substantially influence the differential expression analysis. Furthermore, apart from the primary factor of interest and unforeseen artifacts, an RNA-seq experiment typically contains multiple measured covariates, some of which may significantly affect gene expression levels, while others may not. Existing methods either address the covariate selection or the unknown artifacts separately. In this study, we investigate two integrated strategies, FSR_sva and SVAall_FSR, …

Individual And Collective Properties Of Tunable Photochemical Belousov-Zhabotinsky Micro-Reactors, Kudakwashe Benedict Shumba

Graduate Theses, Dissertations, and Problem Reports (ETD)

Cell-like model chemical systems are powerful tools that can be used to explore the role of intercellular coupling on population level behaviors in communities of biological cells. Firstly, we present a new method for fabricating such micro-reactors using the photosensitive Belousov–Zhabotinsky (BZ) reaction system employed in silica microparticles. These BZ micro-reactors have a tunable response to photochemical coupling, varying from a fully excitatory response to a fully inhibitory response. Their response can be tuned through variations in either the reactive mixture or, on an individual micro-reactor level, by changes in the synthesis temperature used during the fabrication of the silica …

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 …

(R2108) Global Asymptotic Stability Analysis Of Discrete Time Population Model With Allee Effect Through Lyapunov Function, Govind Jha, Neeraj Kumar, Sarita Jha

Applications and Applied Mathematics: An International Journal (AAM)

This study explores the idea of stability analysis by using Lyapunov functions in discrete time population models; this work focuses on the nth generation. Further, this investigation aims to extend global stability concepts to discrete-time models and considers the influence of the Allee effect on population dynamics. Mathematical formulations and specific modelling approaches are utilized to investigate the behavior of the population system. The results reveal a larger range of stability in comparison to previous findings, emphasizing the effectiveness of the Lyapunov function approach. Specifically highlighted here are the extension of global stability concepts to the nth generation providing insights …

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.

Shevtsov: Growing Pains And Growing Gains: The Arizona Experience, Tynan Lazarus, Jane Shevtsov

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Early Ctdna Kinetics As A Dynamic Biomarker Of Cancer Treatment Response, Aaron Li, Emil Lou, Kevin Leder, Jasmine Foo

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Kreig: Examining Affinity Maturation And Antigenic Drift With An Agent-Based Model, Jasmine Af Kreig, Jannatul Ferdous, Ruian Ke, Ruy M. Ribeiro

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.