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    Potential Scenario
    109

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    40

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    2011-Therese-Keane-Combat modelling with partial differential equations
    We present work seeking to more realistically represent troop dynamics and to enable a deeper understanding of the nature of conflict.
    Lanchester modeltroop dynamicsswarming behaviortroop regroupinglossesnon-local termslocal terms
    Modeling Scenario
    461

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    129

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    6-017-OncolyticViruses-ModelingScenario
    Students explore oncolytic virotherapy using systems of differential equations and numerical simulations.
    cancercancer-immune dynamicsimmune suppressor drugoncolytic virusvirotherapy
    Potential Scenario
    194

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    60

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    2013-Gonzalez_Parra-Arenas-Mathematical Model for Social Security Systems with Dynamical Systems
    In this paper it is proposed a mathematical approach based on dynamic systems to study the effect of the increase in the Social Security normal retirement age on the worker and on the dynamics of retiree populations.
    dynamical systemsretirement modelSocial Security
    Potential Scenario
    214

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    69

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    2019-Ekici_Plyley. Inquiry-Based_Modeling_of_Population_Dynamics_With_Logistic_Differential_and_Difference_Equations
    Inquiry-based learning activities on modeling and controlling the growth of locally relevant species, such as lionfish or sea turtles, are developed by the authors.
    population dynamicslogisticInquiry-based modelingIBL
    Modeling Scenario
    320

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    335

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    5-024-PhGreatLakes
    In this teaching modeling scenario, we demonstrate how lessons on salt-tank compartmental modeling can be used to predict phosphorus levels in the Great Lakes.
    Great Lakeslimnologycomparmentpollutioncompartmental modelsphosphorous
    Modeling Scenario
    321

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    487

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    6-016-PandemicModeling-ModelingScenario
    The recent coronavirus outbreak has infected millions of people worldwide and spread to over 200 countries. How can we use differential equations to study the spread of coronavirus?
    population dynamicsinfectious diseasediseaseEbolaeSIR modelsCOVID19pandemicepidemicreproduction number
    Potential Scenario
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    111

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    2017-Biswasa-EtAl-Mathematical Modeling Applied to Sustainable Management of Marine Resources
    We study a nonlinear mathematical model of fishery management to understand dynamics of a fishery resource system in an aquatic environment that consists of two zones; one free fishing zone and another reserve zone where fishing is strictly...
    natural resourcesmarine resourcesfishery model
    Potential Scenario
    182

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    80

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    2011-Nakul-Chitnis-Introduction to Mathematical Epidemiology - Deterministic Compartmental Model
    Deterministic compartmental models form the simplest models in the mathematical study of infectious disease dynamics. They assume that a population is homogenous (all people are the same) and the only distinction is in their disease state.
    sensitivitydiseaseinfectionthresholdcompartmentbifrucation
    Potential Scenario
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    49

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    2010-Shaza_Hussein-Predator-Prey Modeling
    The objective of this project was to create five projections of animal populations based on a simple predator-prey model and explore the trends visible.
    population dynamicspredator-preylogistic equationEndangered Catsdecreasing populationrabbitsfoxes
    Potential Scenario
    129

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    55

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    2001-Tsoularis-Analysis of logistic growth models
    variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. We further review and compare several such models.
    logisticGompertzVerhulstPearl and ReedBertalanffy
    Modeling Scenario
    222

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    457

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    0

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    5-002-RelationshipDynamics-ModelingScenario
    The different possible dynamics of a two-person romantic relationship are modeled -- as a linear two dimensional system of equations -- and analyzed.
    love affairRomeo and Juliet
    Free Online Textbook
    210

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    77

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    0

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    2016-Rob_deBoer-Population Dynamics  A Graphical Approach
    This book is an introduction into modeling population dynamics in ecology. Because there are several good textbooks on this subject, the book needs a novel ecological niche to justify its existence.
    mathematical modelstabilitycompetitionSIRbifurcationconsumptionpopulation population dynamicsgeneral replicationnonlinear density dependenciesfunctional responsepersistencephase plan analysis
    Article or Presentation
    940

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    86

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    SIMIODE Spring 2024 Webinars - Insightmaker
    We discuss the use of the FREE system dynamics software Insightmaker (https://insightmaker.com/) in a first course in Ordinary Differential Equations (with a modeling emphasis).
    modelingsimulationSoftwarepythonsystemsInsightMakerflowCategory Theorystockstock-flow
    Potential Scenario
    167

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    60

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    2006-Michael_Coleman-Population Modeling with Ordinary Differential Equations
    We will investigate some cases of differential equations population models beyond the separable case and then expand to some basic systems of ordinary differential equations.
    population dynamics
    Modeling Scenario
    408

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    279

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    1-024-MalariaControl-ModelingScenario
    This project offers students a chance to make policy recommendations based on the analysis of models using both linear (exponential decay) and non-linear (logistic growth) differential equations.
    population dynamicsmalariaPolicyDecision-makingEuler's methodpharmacokineticsmosquitoimproved Euler's methodHuen's methodUS Army
    Modeling Scenario
    453

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    180

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    1-039-StochasticPopModels-ModelingScenario
    We develop strategies for creating a population model using some simple probabilistic assumptions. These assumptions lead to a system of differential equations for the probability that a system is in state (or population size) n at time t.
    Probabilitypopulation dynamicsVarianceMeanstochasticdeterministic
    Modeling Scenario
    300

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    133

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    1-118-SolowEconomicGrowth-ModelingScenario
    Students construct and analyze the celebrated Solow-Swan model of economic growth theory. The project is divided into three sequential parts to teach students to understand, develop, and analyze a simple nonlinear model of economic dynamics.
    optimizationeconomicssteady stategrowthSolow-Swan modelcapitalproductionlaborGolden Rule of Economic Growth
    Modeling Scenario
    274

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    133

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    1-143-PopulationModelVariationsMATLAB-ModelingScenario
    Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models.
    population dynamicsecologylogistic growthbifurcation theoryslope fieldsextinctionharvestingqualitative analysisstocking
    Modeling Scenario
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    209

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    6-018-ExploringSIRModel-ModelingScenario
    Students will transform, solve, and interpret Susceptible Infected Recovered (SIR) models using systems of differential equation models. The project is progressively divided into three parts to understand, to apply, and to develop SIR models.
    population dynamicssensitivitydiseaseSIR modelsepidemicrumors
    Modeling Scenario
    393

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    610

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    6-022-CannibalismPredatorPrey-ModelingScenario
    The Lotka-Volterra model tells us that the prey and predator exhibit a shifted cyclic behavior over time. In this module, we look at modifying this prey-predator model to consider the case when there is cannibalism in the predator species.
    stabilitypredator-preyequilibriaoscillationscannibalismphase planesspiral sinks