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    Modeling Scenario
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    5-001-LSD-ModelingScenario
    We describe the use of a two compartment model of a linear system of first order linear differential equations to model lysergic acid diethylamide (LSD) in the body. We provide the data from the literature.
    LSDSpanishcompartmentpharmacokineticslysergic acid diethylamide
    Modeling Scenario
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    1-132-DigoxinElimination-ModelingScenario
    We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
    nullclinespharmacokineticsdigoxindrug eliminationtwo compartment
    Modeling Scenario
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    1-086-MedicinalPill-ModelingScenario
    Administration of a medicinal pill in single and multiple doses is modeled.
    medicinespillovercompartmentbloodstreamGIT-Track
    Modeling Scenario
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    5-020-ParacetamolAbsorption-ModelingScenario
    We offer drug absorption data on paracetamol, an analgesic pain reliever, for two different sets of patients, vegetarian and non-vegetarian. Students build a two compartment model for plasma and non-plasma (tissue) compartments of human patients.
    paracetamolanalgesicvegetariannon-vegetarian
    Modeling Scenario
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    5-026-Evictions-ModelingScenario
    In this project, students develop two SIS models to study eviction trends in a population of non-homeowner households using an actual eviction rate. Students can calculate solutions, sketch the phase portrait, and determine long-term trends .
    carrying capacitycompartmentevictionhomeownerSIS modelhomelessness
    Modeling Scenario
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    6-029-TumorGrowth-ModelingScenario
    This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of tumor growth over time.
    Pop_Growth Pilotlogisticcomparmenttumorsynthetic datasum of squares error
    Modeling Scenario
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    5-012-LipoproteinModeling-ModelingScenario
    Data from a study on the amounts of low-density-lipoprotein (LDL), form of cholesterol, in blood plasma is presented. Students build, validate, and use a compartment model of the kinetic exchange of the LDL between body tissue and blood plasma.
    wildlifelow-density-lipoproteintracercompartment modelcholesterolblood plasmabody tissue
    Modeling Scenario
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    1-025-MixingItUp-ModelingScenario
    Students build three different models for levels of salt in a tank of water and at each stage the level of complexity increases with attention to nuances necessary for success.
    compartmentsalttankmixing
    Modeling Scenario
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    5-025-SaltCompartments-ModelingScenario
    Model a phenomena in which salt mixtures from two tanks are mixed using several strategies.
    compartmentsalttanks
    Modeling Scenario
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    5-005-Dialysis-ModelingScenario
    We design a compartment model of a kidney dialysis machine and compare 3 and 9 compartments for the machine as well as determine the effect of change in one of the parameters in the model on the effectiveness to deliver quality dialysis.
    countercurrent multiplierkidneydialysisconcurrentcompartment
    Modeling Scenario
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    1-085-DrugBolus-ModelingScenario
    Given data on the concentration of a drug in the plasma of a human in mg/L at certain time intervals in hours can we determine the rate at which the drug leaves the plasma as well as the initial amount administered in a intravenous bolus of the drug?
    concentrationsum of square errorsbolusdrugrate constantadminister
    Modeling Scenario
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    1-051-OneTankSaltModel-ModelingScenario
    A large tank initially contains 60 pounds of salt dissolved into 90 gallons of water. Salt water flows in at a rate of 4 gallons per minute, with a salt density of 2 pounds per gallon. The incoming water is mixed in with the contents of the tank...
    compartmentsalttankmixingflow
    Modeling Scenario
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    1-065-AlgalBlooms-ModelingScenario
    This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, starting in 1994.
    direction fieldstool:dfieldalgaeharmful algae bloomspopulationcompartmentLake Chapala
    Modeling Scenario
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    1-134-LanguageDynamics-ModelingScenario
    Students will be introduced to a mathematical model for language dynamics. Specifically, the model describes the change in the fraction of a population speaking one language over another.
    languagecompartmentphase linesbifurcationswitching
    Modeling Scenario
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    1-042-KoolAid-ModelingScenario
    Students run experiments involving concentrated solution of drink powder flowing from upper to lower tank, initially filled with plain water. They make qualitative observations about the intensity of the color in the tanks, record data, and build...
    concentrationcompartmenttanksKoolAid
    Modeling Scenario
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    5-011-ModelingIbuprofren-ModelingScenario
    We consider modeling of data from a clinical experiment administered as oral doses of 400 mg ibuprofen, an analgesic pain reliever. Concentrations of ibuprofen in the serum/plasma of the subjects were recorded after the initial ingestion of the...
    dataAICAkaike Information Criterionabsorptionsum of square errorscompartment modelibuprofendelay
    Modeling Scenario
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    6-007-FunctionsAndDerivativesInSIRModels-ModelingScenario
    Given a system of differential equations, how do the solution graphs compare with the graphs of the differential equations? Students tackle this question using SIR models for well-known infectious diseases.
    epidemiologyspecies interactionsderivativesvisualizationinfectionSIR modelsLaw of Mass Action
    Modeling Scenario
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    6-020-AlgaePopulationSelf-Replenishment-ModelingScenario
    This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, in 1994. A
    algaepopulationMexicoqualitativecompartmentlinearizationJacobianlaknondimensionalizationpplane
    Modeling Scenario
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    1-035-DotseroVolcanoEruption-ModelingScenario
    In this scenario, we use Carbon-14 dating of the Dotsero volcano in Colorado as a way of emphasizing this multistage process of modeling.
    exponential decayhalf-lifedecayEuler's methodcarbon datingdecay rateCarbon-14Dotsero volcanovolcano
    Modeling Scenario
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    5-014-TwoSpringMass-ModelingScenario
    We ask students to build a Free Body Diagram for a vertical two mass situation in which the two masses are held fixed at the tip and at the bottom. The mass holds the springs together at the join of the two springs in between.
    massspring mass dampersprings