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    1999-PS_Crooke-S_Hota_JJ_Martini-JR_Hochkiss-A Mathematical Model for Carbon Dioxide Exchange
    A mathematical model is presented to study the effect of Tracheal Gas Insufflation (TGI) on the alveolar ventilation during passive, mechanical ventilation.

    Keywords: mechanical ventilationventilationcarbon dioxide exchangetracheal gas insufflationalveolar ventilationshunttwo-compartment model

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    6-004-VillageEpidemic-ModelingScenario
    Students are offered data from a plague epidemic that occurred in the middle of the seventeenth century in Eyam, a small English village. With only two assumptions offered to students they...

    Keywords: SIR modelsepidemicsusceptibleinfectiveremovedEyamEnglish village

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    1-030-EyeModel-ModelingScenario
    We offer a mathematical modeling experience using differential equations to model the volume of an intraocular gas bubble used by ophthalmologists to aid the healing of a surgically repaired region...

    Keywords: retinal surgeryAkaike Information CriterionSpanishsum of square errorssurgeryretionaophthalmologyeyeintraocular gas bubble

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    3-006-Buoyancy-ModelingScenario
    We offer data from a physical experiment in which the depth of a container in water is measured and ask students to build a model of buoyancy based on Newton's Second Law of Motion and a Free Body...

    Keywords: data collectionexperimentbuoyancyNewton's Second Law of Motion

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    3-017-StackedCoffeeFiltersFalling-ModelingScenario
    Data on free falling 2, 4, 6, and 8 stacked coffee filters is offered. Students form a model using a resistance term proportional to velocity, velocity squared, or velocity to some general power....

    Keywords: dataresistancefalling bodycoffee filterstacked

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    3-019-ShuttleCockFalling-ModelingScenario
    We are given data on the time and position of a shuttlecock as it falls to the ground from a set height. We attempt to model the falling object and we confront the different resistance terms and...

    Keywords: resistancegravityFree Body Diagramshuttlecockfallingc object

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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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    5-023-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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    5-077-MandMAttritionWarfare-ModelingScenario
    Students model attrition between two opposing forces using M&M candies and discover a system of linear differential equations of order one, often called the Lanchester equations.

    Keywords: attritionLanchester modelpredator-predatorN-square Law

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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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    6-067-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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    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...

    Keywords: countercurrent multiplierkidneydialysisconcurrentcompartment

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    A Critical Guide to BLAST
    This Critical Guide in the Introduction to Bioinformatics series provides an overview of the BLAST similarity search tool, briefly examining the underlying algorithm and its rise to popularity.

    Keywords: NIBLSEBLASTGOBLETInstructorResources

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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.

    Keywords: vaccinationinfectionSIRepidemic

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    2007-Zenker-Rubin-Clermont-From inverse problems in mathematical physiology to quantitative differential diagnoses
    The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data...

    Keywords: physiologyinverse problem

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    1972-R_C_Rothermel-A Mathematical Model for Predicting Fire Spread in Wildland Fuels
    The development of a mathematical model for predicting rate of fire spread and intensity applicable to a wide range of wildland fuels is presented from the conceptual stage through evaluation and...

    Keywords: predictionforest firefire managementfire spreadfuel

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    6-005-InsectColonySurvivalOpt-ModelingScenario
    We present a system of nonlinear differential equations to model the control of energy flow into producing workers or reproducers in an insect colony, using a set of given parameters and a number...

    Keywords: optimizationOptimal Control Theoryinsect colonyoptimal controlnatural resourcesPointryagin's Maximum Principlecontrol variable

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    2017-Adolfo_Rumbos-Differential Equations and modeling
    The study of any phenomenon in the physical or biological sciences, in which continuity and differentiability assumptions about the quantities in question can be made, invariably leads to a...

    Keywords: pendulumLotka Volterra equationsexistenceuniqueness

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    2016-Bonin-EtAl-Mathematical modeling based on ordinary differential equations-vaccinology
    We developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature.

    Keywords: Immunologyimmune systemAntigenvaccinologyyellow fever

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