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Infusing Quantitative Reasoning Skills Into A Differential Equation Class In An Urban Public Community College, Tanvir Prince 2024 CUNY Hostos Community College

Infusing Quantitative Reasoning Skills Into A Differential Equation Class In An Urban Public Community College, Tanvir Prince

Numeracy

This research centers on implementing Quantitative Reasoning (QR) within a differential equations course at an urban public community college. As a participant in the Numeracy Infusion for College Educators (NICE) faculty development program, I sought to integrate QR skills into my curriculum. Students in the course were introduced to QR goals using real-world data sets, particularly those related to population growth, which aim to enhance their understanding, sharpen their problem-solving abilities, and cultivate a positive perspective on the real-world relevance of mathematics. Preliminary findings indicate varied levels of QR skill development among students. These results underscore the potential benefits of …


A Tale Of Two Viruses: Why Smallpox Was Eradicated And Polio Persists, Katherine G. McGough, Erin N. Bodine 2024 Rhodes College

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 …


A Coupled Model Of Population, Poaching, And Economic Dynamics To Assess Rhino Conservation Through Legal Trade, Henry Doyle, Kylie Champagne, Ditto Rajpal, Grace Seebeck, David J. Gerberry 2024 Xavier University

A Coupled Model Of Population, Poaching, And Economic Dynamics To Assess Rhino Conservation Through Legal Trade, Henry Doyle, Kylie Champagne, Ditto Rajpal, Grace Seebeck, David J. Gerberry

Spora: A Journal of Biomathematics

Rhinoceros populations in Africa are in peril largely due to the high value of their horns and the poaching that ensues. The strategy of legalizing the international trade of rhino horn is receiving increased support among both the people and government officials in Africa. Many in the international conservation community remain opposed to the idea. The legalization strategy is straightforward in theory: legalizing the trade of rhino horn will introduce a large quantity of horn to the market, the increased supply will lead to lower prices for rhino horn, and lower prices will reduce the overall poaching pressure these animals …


Odes And Mandatory Voting, Christoph Borgers, Natasa Dragovic, Anna Haensch, Arkadz Kirshtein, Lilla Orr 2024 Tufts University, Medford, MA

Odes And Mandatory Voting, Christoph Borgers, Natasa Dragovic, Anna Haensch, Arkadz Kirshtein, Lilla Orr

CODEE Journal

This paper presents mathematics relevant to the question whether voting should be mandatory. Assuming a static distribution of voters’ political beliefs, we model how politicians might adjust their positions to raise their share of the vote. Various scenarios can be explored using our app at https: //centrism.streamlit.app/. Abstentions are found to have great impact on the dynamics of candidates, and in particular to introduce the possibility of discontinuous jumps in optimal candidate positions. This is an unusual application of ODEs. We hope that it might help engage some students who may find it harder to connect with the more customary …


Fitting A Covid-19 Model Incorporating Senses Of Safety And Caution To Local Data From Spartanburg County, South Carolina, D. Chloe Griffin, Amanda Mangum 2024 Brown University

Fitting A Covid-19 Model Incorporating Senses Of Safety And Caution To Local Data From Spartanburg County, South Carolina, D. Chloe Griffin, Amanda Mangum

CODEE Journal

Common mechanistic models include Susceptible-Infected-Removed (SIR) and Susceptible-Exposed-Infected-Removed (SEIR) models. These models in their basic forms have generally failed to capture the nature of the COVID-19 pandemic's multiple waves and do not take into account public policies such as social distancing, mask mandates, and the ``Stay-at-Home'' orders implemented in early 2020. While the Susceptible-Vaccinated-Infected-Recovered-Deceased (SVIRD) model only adds two more compartments to the SIR model, the inclusion of time-dependent parameters allows for the model to better capture the first two waves of the COVID-19 pandemic when surveillance testing was common practice for a large portion of the population. We find …


Modeling Aircraft Takeoffs, Catherine Cavagnaro 2024 Sewanee University

Modeling Aircraft Takeoffs, Catherine Cavagnaro

CODEE Journal

Real-world applications can demonstrate how mathematical models describe and provide insight into familiar physical systems. In this paper, we apply techniques from a first-semester differential equations course that shed light on a problem from aviation. In particular, we construct several differential equations that model the distance that an aircraft requires to become airborne. A popular thumb rule that pilots have used for decades appears to emanate from one of these models. We will see that this rule does not follow from a representative model and suggest a better method of ensuring safety during takeoff. Aircraft safety is definitely a matter …


Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen 2024 Wilfrid Laurier University

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …


Analyzing A Smartphone Battle Using Bass Competition Model, Maila Hallare, Alireza Hosseinkhan, Hasala Senpathy K. Gallolu Kankanamalage 2023 United States Air Force Academy

Analyzing A Smartphone Battle Using Bass Competition Model, Maila Hallare, Alireza Hosseinkhan, Hasala Senpathy K. Gallolu Kankanamalage

CODEE Journal

Many examples of 2x2 nonlinear systems in a first-course in ODE or a mathematical modeling class come from physics or biology. We present an example that comes from the business or management sciences, namely, the Bass diffusion model. We believe that students will appreciate this model because it does not require a lot of background material and it is used to analyze sales data and serve as a guide in pricing decisions for a single product. In this project, we create a 2x2 ODE system that is inspired by the Bass diffusion model; we call the resulting system the Bass …


Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia 2023 Brigham Young University

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …


Nonsmooth Epidemic Models With Evolutionary Game Theory, Cameron Morin 2023 University of Maine

Nonsmooth Epidemic Models With Evolutionary Game Theory, Cameron Morin

Electronic Theses and Dissertations

This thesis explores the utilization of game theory and nonsmooth functions to enhance the accuracy of epidemiological simulations. Traditional sensitivity analysis encounters difficulties when dealing with nondifferentiable points in nonsmooth functions. However, by incorporating recent advancements in nonsmooth analysis, sensitivity analysis techniques have been adapted to accommodate these complex functions. In pursuit of more accurate simulations, evolutionary game theory, primarily the replicator equation, is introduced, modeling individuals’ decision making processes when observing others’ choices. The SEIR model is explored in depth, and additional complexities are incorporated, leading to the creation of an expanded SEIR model, the Be-SEIMR model.


(R2056) Convergence Criteria For Solutions Of A System Of Second Order Nonlinear Differential Equations, Akinwale Olutimo 2023 Lagos State University

(R2056) Convergence Criteria For Solutions Of A System Of Second Order Nonlinear Differential Equations, Akinwale Olutimo

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we investigate the convergence of solutions of certain nonlinear system of two differential equations using a suitable Lyapunov functional with sufficient conditions to establish our new result. An example is given to demonstrate the effectiveness of the result obtained and geometric argument to show that the solutions of the system are better rapidly converging under the criteria obtained.


Game-Theoretic Approaches To Optimal Resource Allocation And Defense Strategies In Herbaceous Plants, Molly R. Creagar 2023 University of Nebraska-Lincoln

Game-Theoretic Approaches To Optimal Resource Allocation And Defense Strategies In Herbaceous Plants, Molly R. Creagar

Department of Mathematics: Dissertations, Theses, and Student Research

Empirical evidence suggests that the attractiveness of a plant to herbivores can be affected by the investment in defense by neighboring plants, as well as investment in defense by the focal plant. Thus, allocation to defense may not only be influenced by the frequency and intensity of herbivory but also by defense strategies employed by other plants in the environment. We incorporate a neighborhood defense effect by applying spatial evolutionary game theory to optimal resource allocation in plants where cooperators are plants investing in defense and defectors are plants that do not. We use a stochastic dynamic programming model, along …


Controlled Manipulation And Transport By Microswimmers In Stokes Flows, Jake Buzhardt 2023 Clemson University

Controlled Manipulation And Transport By Microswimmers In Stokes Flows, Jake Buzhardt

All Dissertations

Remotely actuated microscale swimming robots have the potential to revolutionize many aspects of biomedicine. However, for the longterm goals of this field of research to be achievable, it is necessary to develop modelling, simulation, and control strategies which effectively and efficiently account for not only the motion of individual swimmers, but also the complex interactions of such swimmers with their environment including other nearby swimmers, boundaries, other cargo and passive particles, and the fluid medium itself. The aim of this thesis is to study these problems in simulation from the perspective of controls and dynamical systems, with a particular focus …


Long-Acting Cabotegravir And The Emergence Of Drug-Resistant Hiv, Katharine Gurski 2023 Howard University

Long-Acting Cabotegravir And The Emergence Of Drug-Resistant Hiv, Katharine Gurski

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Utilizing Non-Negative Least Squares For Data-Driven Discovery Of Dynamics, Tracey G. Oellerich 2023 George Mason University

Utilizing Non-Negative Least Squares For Data-Driven Discovery Of Dynamics, Tracey G. Oellerich

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Effect Of Under-Reporting, Vaccine Efficiency And Social Behavior On Epidemic Progression, Samiran Ghosh, Samiran Ghosh 2023 Illinois State University

Effect Of Under-Reporting, Vaccine Efficiency And Social Behavior On Epidemic Progression, Samiran Ghosh, Samiran Ghosh

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Baa-Ttling Sore Mouth In Sheep With Mathematical Modeling, David C. Elzinga, W. Christopher Strickland 2023 University of Wisconsin-La Crosse

Baa-Ttling Sore Mouth In Sheep With Mathematical Modeling, David C. Elzinga, W. Christopher Strickland

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 2023 Virginia Commonwealth University

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.


Incorporating Adaptive Human Behavior Into Epidemiological Models Using Equation Learning, Austin Barton, Jordan Klein, Jonathan Greer, Kevin Flores, Patrick Haughey 2023 Georgia Institute of Technology - Main Campus

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.


Understanding Impact Of Educational Awareness And Vaccines As Optimal Control Mechanisms For Changing Human Behavior In Disease Epidemics, Manal Badgaish, Dr. Padmanabhan Seshaiyer 2023 George Mason University

Understanding Impact Of Educational Awareness And Vaccines As Optimal Control Mechanisms For Changing Human Behavior In Disease Epidemics, Manal Badgaish, Dr. Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


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