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    Modeling Scenario
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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
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    1-066-USCensusModeling-ModelingScenario
    The United States Census, conducted every 10 years, gives data on the United States population, that can be modeled with the exponential, logistic, or Gompertz functions.
    datalogisticpopulationGompertzcensusgoodness of fit
    Modeling Scenario
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    1-124-WorldPopulation-ModelingScenario
    We build models of world population using data to estimate growth rate.
    population dynamicshumangrowth ratevarying growth rate
    Modeling Scenario
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    1-170-CensusModeling-ModelingScenario
    Students who have studied models for population are likely to be familiar with the exponential and the logistic population models. The goal here is to explore the role of modeling assumptions in choosing which model to use.
    logistic growthexponentialpopulationU.S. Census DataassumptionGoogle SheetsUnites StatesGuatemala
    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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    3-087-ThanosPopulationDynamicsInteractingSpecies-ModelingScenario
    Thanos snaps his fingers and turns half of all living creatures to dust with the hope of restoring balance to the natural world. How does this affect the long term behavior of various species?
    species interactionspredator-preycompetitionLotka-Volterrasensitivity analysisdynamicspopulation
    Modeling Scenario
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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.
    continuousimmigrationpopulationdeathdiscrete
    Modeling Scenario
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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.
    ecologyclimate changeinsectinsect outbreaksinsect outbreaksolitary wave
    Modeling Scenario
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    6-025-WhalesAndKrill-ModelingScenario
    Students will use Excel to observe qualitative behavior in a simulation of a predator-prey model, with blue whales and krill as the predator and prey populations, respectively.
    krillwhalepredatpr-prey
    Modeling Scenario
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    1-087-ThanosPopulationDynamics-ModelingScenario
    In the end of the “Avengers Infinity War,” the villain Thanos snaps his fingers and turns half of all living creatures to dust with the hope of restoring balance to the natural world. How does this affect the long term behavior of various species?
    logisticexponentialpopulationThanos
    Modeling Scenario
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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
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    1-021-FeralCatControl-ModelingScenario
    Students act as professional mathematical consultants and write a report analyzing the client's problem. The client company is a fictional organization which advocates for the use of trap-neuter-return (TNR) as a control method for feral cat...
    population growthcontrolferal catspopulation controlneutertrap-killtrap-neuter-return
    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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    1-067-ModelingWithSigmoidCurves-ModelingScenario
    The assignment considers two well-known models of population growth, Verhulst-Pearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or S-shape.
    logisticGompertzsigmoidVerhulst-Pearl
    Modeling Scenario
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    1-091-InvestigatingSlopeFields-ModelingScenario
    Students will gain experience writing differential equations to model various population scenarios, they will create slope fields to view the solution curves using software, and they will discuss the behavior of the solution curves.
    slope fieldspopulation
    Modeling Scenario
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    1-135-FishHarvesting-ModelingScenario
    This short activity will walk students through a guided list of questions to help them to understand how the stability of equilibrium changes with changes in a model parameter, in this case the rate of harvesting fish.
    population dynamicsfishstabilitybifurcationharvest
    Modeling Scenario
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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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    9-005-InvasiveSpeciesModel-ModelingScenario
    This scenario takes students through the development of an invasive species partial differential equation model. Basic models are discussed first, which lead students to eventually develop their own model which takes into account dispersion.
    Invasive Specieslogisticmigrationtraveling wavesdispersion
    Modeling Scenario
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    1-119-DairyFarming-ModelingScenario
    A simple first order population growth model is presented. The challenge is to produce a final differential equation which is the result of the difference or ratio of birth and death rates. This ratio is not immediately intuitive.
    population dynamicsdairyfarmers' marketsgrowthcow
    Modeling Scenario
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    1-190-IntroClass-ModelingScenario
    Students go through development of ideas in mathematical modeling with differential equations. They encounter fundamental ideas of unlimited population growth, limited population growth and a predator prey system.
    population dynamicspredator-preylogisticexponentialgraphical interpretationsqualitative analysis