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    1-111-SpreadOfInformation-ModelingScenario
    Students perform experiments to model spread of information within a population. Students collect data, determine essential components and parameters and build a mathematical model culminating with...

    Keywords: datalogisticracismprejudicemisinformationmemesspreaddisinformationinformationliesGoogle Trendscoinspennies

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    1-137-SheepGraze-ModelingScenario
    In this activity, students will apply graphical analysis (such as phase lines) to determine the long-term predictions of a differential equation model for pasture grass using two different formulas...

    Keywords: herbivoreplantphase linesbifurcationoverexploitationsheepgraze

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    1-139-PlantsVsHerbivores-ModeliongScenario
    In this activity, students will apply a variety of techniques for analyzing nonlinear systems (e.g., nullclines, linearization, and technologies for drawing phase portraits) to study...

    Keywords: ecologynullclinesherbivoreplant-herbivore interactionsplantlinearization

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    1-001a-MMDeathImmigration-Variation-ModelingScenario
    We model exponential death with m&m's as well as death with immigration.

    Keywords: simulationdatam&mimmigrationdeath

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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...

    Keywords: dataAICAkaike Information Criterionabsorptionsum of square errorscompartment modelibuprofendelay

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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...

    Keywords: wildlifelow-density-lipoproteintracercompartment modelcholesterolblood plasmabody tissue

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    5-023-FakingGause-ModelingScenario
    We use a fake or toy data set to permit discovery of the parameters in a two population protozoan model used to study paramecium and yeast competition in the 1930's studies of G. F. Gause in the...

    Keywords: competitionlogisticyeastGauseparameciumpoplulation

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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...

    Keywords: epidemiologyspecies interactionsderivativesvisualizationinfectionSIR modelsLaw of Mass Action

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    6-015-CombatingEbolaEpidemic-ModelingScenario
    This project offers students a chance to make a policy recommendation based on analysis of a nonlinear system of differential equations (disease model). The scenario is taken from the fall of 2014...

    Keywords: diseaseEbolaAnalysisPolicydecision

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    6-019-EnablingEpidemicExploration-ModelingScenario
    We became aware of several interesting possibilities for a modeling opportunity with data and we invited you to explore the several routes to parameter estimation in a SIR model with respect to the...

    Keywords: Akaike Information CriterionMichaelis-Mentenepidemicsaturationgradientleast sum of square errors

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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

    Keywords: algaepopulationMexicoqualitativecompartmentlinearizationJacobianlaknondimensionalizationpplane

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    6-045-CholeraTranmission-ModelingScenario
    During the project described here, the students will learn how to solve and address a practical problem such as cholera transmission using various mathematical tools.

    Keywords: infectious diseasecholeraendemicdisease-freetransmission ratewaterborne pathogen

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    6-065-InternetPlatformUsers-ModelingScenario
    A model estimating the volume of users interacting through a two-sided Internet platform (allowing interaction of two types of users) will teach students how to analyze a 2-dimensional dynamical...

    Keywords: dynamicsflowconservedfixed pointscycletinternet platformdiverghenceJacobianattractingrepellingnodesstablesaddlespiral

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    6-067-LotkaVolterra-ModelingScenario
    This modeling scenario guides students through the process of fitting the Lotka-Volterra model of two differential equations to a real time series observational data. Students use the capabilities...

    Keywords: time seriesdatacompetitionLotka-Volterramodel fittingpredictiongauseRexperimental

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    1-009-ICUSpread-ModelingScenario
    We offer students the opportunity to model the percentage of voluntary nonprofit hospitals in the United States with Intensive Care Units during the period of 1958-1974.

    Keywords: logisticsum of square errorsIntensive Care Unithospitalspread

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    1-004-MicroorganismImmigration-ModelingScenario
    We present a modeling opportunity for population death with non-constant immigration and suggest the use of both discrete and continuous models with a comparison of results.

    Keywords: continuousimmigrationpopulationdeathdiscrete

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    10-100-InsectOutbreaks-ModelingScenario
    We use a system of difference equations that incorporates a temperature-dependent MPB population growth rate to model the outbreak and recovery cycle in mountain pine beetle-infested forests.

    Keywords: ecologyclimate changeinsectinsect outbreaksinsect outbreaksolitary wave

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    1-127-FishHarvesting-ModelingScenario
    We offer students a harvesting model for operating a fishery over a 25 year horizon and ask them to write a report on optimal harvesting policy with their analyses for fishing industry experts (not...

    Keywords: Management Of Dataoptimal controlfisherieslogisticharvestingmaximum sustainable yield

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    1-037-CommonColdSpread-ModelingScenario
    This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more...

    Keywords: diseasecommon coldresidence hall

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    6-040-StruggleForExistence-ModelingScenario
    We use historical data from the 1930's in the Soviet Union and model competition between two species of yeast after modeling each species separately and estimate parameters

    Keywords: competitionlogisticcarrying capacityparamecium

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