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    Potential Scenario
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    2014-Wang-EtAl-Estimating Mixed-Effects Differential Equation Models
    When multiple replicates of measurements are available for the dynamic process, it is of great interest to estimate mixed-effects in the ODE model for the process. We propose a semiparametric method to estimate mixed-effects ODE models.
    pharmacokineticsdynamic modelssmoothingsplinemixed-effects modelsHiV combination therapy
    Potential Scenario
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    2008-Huangi-Lu-Modeling long-term longitudinal HIV dynamics with applications to an AIDS clinical study 
    To better understand the factors responsible for the virological failure, this paper develops the mechanism-based nonlinear differential equation models for characterizing long-term viral dynamics with ARV therapy.
    longitudinal dataAIDSantiretroviral drug therapyBayesian nonlinear mixed-effectstime-varying drug efficacyHIV dynamics
    Potential Scenario
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    2009-Su-EtAl-Fitting Compartmental Models to Multiple Dose Pharmacokinetic Data using SAS
    In the case of a multiple dose study where subjects experience different dosing times, a superposition principle can be used to recursively account for each additional dose.
    SASsuperpositionpharmacokineticscompartmental modelsmultiple dose
    Potential Scenario
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    2009-Noakes-Sleigh-Mathematical models for assessing the role of airflow on the risk of airborne infection in hospital wards
    Understanding the risk of airborne transmission can provide important information for designing safe healthcare environments with an appropriate level of environmental control for mitigating risks.
    infectioncompartmenthospitalventilationairbornesthochasticWells–Riley
    Modeling Scenario
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    115

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    6-028-SaltCompartments-ModelingScenario
    Model a phenomena in which salt mixtures from two tanks are mixed with changing volumes of water.
    concentrationcomparmentsalttankmixing
    Modeling Scenario
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    261

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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
    Potential Scenario
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    2017-Jean-Roux-Mathematical Models in Air Quality Problems
    Presents many models with analysis in air quality control. Starts with chemical kinetics models and builds complexity to PDE models.
    air pollution effects on forest ecosystemsfinite volume methodboundary layerchemical kineticsfinite differenceemissionsdepositionsadvection
    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
    Potential Scenario
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    2013-Fathalla_Rihan-Delay Differential Equations in Biosciences - Parameter estimation and sensitivity analysis
    This is a review article to show that delay differential models have a richer mathematical framework (compared with models without memory or after-effects) and a better consistency with biological phenomena such dynamical diseases and cell growth...
    epidemiologysensitivityImmunologyphysiologyRK-methodstime-lags
    Potential Scenario
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    22

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    2014-John_Cain-Chemical Reaction Kinetics Mathematical Underpinnings
    The usual way of deriving kinetic equations involves application of the principle of conservation of mass in conjunction with the law of mass action. Here, examples of kinetic models for several basic processes are discussed.
    kineticsbiochemical reactionreactantsproducts
    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
    Potential Scenario
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    53

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    2015-Valerie_Billard-Pharmacokinetic-pharmacodynamic relationship of anesthetic drugs - from modeling to clinical use
    The purpose of this short review is to describe the basis of pharmacokinetics and modeling, the concentration-effects relationship, and drug interactions modeling to offer to anesthesiologists and non-anesthesiologists an overview of the rules to...
    anesthesiapharmacokineticspharmacodynamicanesthetic
    Potential Scenario
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    28

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    2004-Denny-Yackel-Temperature Models for Ware Hall
    This paper offers some very nice extended models for cooling off a new office area for a mathematics department.
    Newton's Law of Coolingcoolingoffice building
    Potential Scenario
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    63

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    2014-Eckhoff-EtAl-Fun with maths-exploring implications of mathematical models for malaria eradication
    . In this note, four examples demonstrate both the effects of model structures and assumptions and also the benefits of using a diversity of model approaches fomalaria eradication strategies.
    vaccinemalariamigrationeradicationseasonality
    Modeling Scenario
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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 Soviet Union.
    competitionlogisticyeastGauseparameciumpoplulation
    Potential Scenario
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    2008-Jai-Li-Differential equations models for interacting wild and transgenic mosquito populations
    We formulate and study continuous-time models, based on systems of ordinary differential equations, for interacting wild and transgenic mosquito populations.
    Mosquito borne diseasespopulationsHolling-II-type mating ratestransgenic mosquitoesnonhyperbolic equilibriummosquitoes
    Potential Scenario
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    40

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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
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    2018-Kovacs-Insperger-Retarded neutral and advanced differential equation models for balancing using an accelerometer
    It is shown that slight modeling differences lead to significant qualitative change in the behavior of the system, which is demonstrated by means of the stability diagrams for the different models.
    feedbackAccelerometersfunctional differential equationssemi-discretizationD-subdivision method
    Potential Scenario
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    39

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    2014-Chivers-EtAl-Predator-prey systems depend on a prey refuge
    We present an agent-based model which does not require the factors or constraints of previous models to reproduce all six patterns in persistent populations.
    Individual & Agent Based Modelingpredator-preythink-pair-shareslynxrefugeprey switchingMustela-Clethrionomys systempatter oriented
    Potential Scenario
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    67

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    1975-David_Burghes-Population dynamics An introduction to differential equations
    In this paper a number of population models, which lead to differential equations, are derived. First-order variables separable equations are formulated from the Malthusian population model and its extension to include crowding effects.
    fishpredator-preylogisticpopulationdelaylag