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    Potential Scenario
    98

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    31

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    1977-HI_Freedman-P_Whitman-Mathematical models of population interactions with dispersal
    A system of differential equations is proposed as a model of dispersion between two populations in habitats separated by a barrier.
    predatorbarriertwo populationstwo habitats
    Potential Scenario
    114

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    42

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    2006-Loyd-Wodarz-Drug Resistance in Acute Viral Infections-Rhinovirus as a Case Study
    We develop an epidemiological model that can be used to address the spread of resistance at the population level, and a virus dynamics model that can be used to study the dynamics of virus over the time course of an individual’s infection.
    stabilityresistancevirusdrugepidemic competitionimmune responserhinovirus
    Potential Scenario
    121

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    30

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    2014-Brun-EtAl-An introduction to the mechanics of the lasso
    Here, we study the mechanics of the simplest rope trick, the Flat Loop, in which the rope is driven by the steady circular motion of the roper’s hand in a horizontal plane.
    bifurcationmotionlassorod modelrodeo
    General Resource
    158

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    40

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    2003-Knorrenschild-Gross-Text Books on Mathematical Modeling in Biology
    Text Books on Mathematical Modeling in Biology Compiled from the Internet by Michael Knorrenschild,
    biologyMathematical Biologytextbooktext
    Potential Scenario
    111

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    43

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    2019-Banuelos_Danet_Flores_Ramos-Epidemiological_Math_Model_Approach_To_Political_System_with_Three_Parties
    A nonlinear compartmental model is derived to study the movement between classes of voters with the assumption of a constant population that is homogeneously mixed.
    politicsparametersvotingcompartment modelepidemiological modelequilibriathree-party system
    Potential Scenario
    190

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    85

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    2005-JC_Sprott-Dynamical Models of Happiness
    A sequence of models for the time evolution of one’s happiness in response to external events is described.
    happinessoscillation
    Article or Presentation
    172

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    47

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    2009-Brian_Winkel-Population_modelling_with_MandMs
    Several activities in which population dynamics can be modeled by tossing M&M’s® candy are presented.
    simulationparameter estimationimmigrationdeathdifference equation
    Potential Scenario
    95

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    30

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    2019-Fred_Brauer-The_Final_Size_of_a_Serious_Epidemic
    In an epidemic of a serious disease, there is likely to be behavioral response that decreases the epidemic size considerably.
    epidemicfinal sizebehavioral responseSIER modelrelations
    Technique Narrative
    460

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    235

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    1-010-AtmosphericCO2Bifurcation-TechniqueNarrative
    Students are introduced to the concept of a bifurcation in a first-order ordinary differential equation (ODE) through a modeling scenario involving atmospheric carbon dioxide whish is taken as a parameter and temperature is a function of time.
    carbon dioxideSurface Atmosphere Exchangebifurcationfold bifurcationsaddle node
    Potential Scenario
    190

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    40

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    0

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    2011-Cruz-Aponte-Herrera-Valdez-Mitigating effects of vaccination on influenza outbreaks given constraints in stockpile size and daily administrati
    We present a SIR-like model that explicitly takes into account vaccine supply and the number of vaccines administered per day and places data-informed limits on these parameters.
    vaccinationinfectionSIRepidemic
    Potential Scenario
    109

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    41

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    2003-Bohren-Dimensional analysis-falling bodies--fine art of not solving differential equations
    Dimensional analysis is a simple, physically transparent and intuitive method for obtaining approximate solutions to physics problems, especially in mechanics.
    falling bodydimensional analysisdrag
    Potential Scenario
    198

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    73

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    2017-Xiang_Liu-Mathematical Studies of Optimal Economic Growth Model with Monetary
    In this paper, efforts will be made to study an extended Neoclassic economic growth model derived from Solow-Swan Model and Ramsey-Cass-Koopsman Model.
    Optimal Control TheoryJacobianSolow-Swan modelMonetary policyoptimal economic growth
    Potential Scenario
    98

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    50

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    0

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    2015-Peter_Cumber-Waggling pendulums and visualization in mechanics
    This article describes an equation of motion for a waggling pendulum.
    resonanceinverted pendulummechanicsdamped pendulum
    Potential Scenario
    102

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    61

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    2006-Shigui_Ruan-Delay differential equations in single species dynamics
    In this survey, we shall review various delay differential equations models arising from studying single species dynamics.
    allee_effectdelayed biological systemsfood limitperiodiciityrecruitment modelRegulation of Haematopoiesis
    Potential Scenario
    119

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    41

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    0

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    2006-Ousmane_Mousa_Tessa-Mathematical model for control of measles by vaccination
    In this article, we use a compartmental mathematical model of the dynamics of measles spread within a population with variable size to provide this framework.
    vaccinationcompartmentherd immunitymeaslesoptimal strategy
    Technique Narrative
    452

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    483

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    0

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    5-005-StiffDifferentialEquations-TechniqueNarrative
    This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples. Stiffness is a property that a system of ODE's may posses that make it difficult to solve numerically.
    Euler's methodexplicit methodsimplicit methodsstiffsitffnessstiff differential equationinstability
    Potential Scenario
    132

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    43

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    2018-Weber_Theers_Surmann_Ligges_Weihs-Sensitivity Analysis_of_Ordinary_Differential_Equation_Models
    This report will focus on the sensitivity analysis of ordinary differential equation (ODE) models since they can be used to model so-called Low Frequency Oscillations (LFOs).
    sensitivityregressionparameter estimationsystemlow frequency oscillationsoscillations
    Modeling Scenario
    263

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    226

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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
    273

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    163

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    1-003-CollegeSavings-ModelingScenario
    We present a modeling opportunity for students in which they have to plan and model for saving for a child's complete college education.
    collegesavingsinterest ratecollege costsensitiviyty
    Modeling Scenario
    258

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    100

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    5-036-HalfCarVibration-ModelingScenario
    Vibration vehicle models provide an opportunity to integrate vehicle-based vibrations into a mechanical engineering vibrations course. The project is on a multiple-degree-of-freedom (MDOF) including pitch and bounce of vehicle body on suspension...
    vibrationvehiclehalf-car modelfinite element analysisshock absorberssuspension