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    Potential Scenario
    202

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    2009-Peter-Howard-Modeling With ODE
    This is a set of class notes rich in examples and ideas for modeling. There is some MatLab code in support of some of the activities.
    ratescompetitionpopulationepidemicpendulumcarbon datingreaction chemistrymechanicsplanetary motiondrag racingHamilton’s methodvariational method
    Potential Scenario
    182

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    49

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    2012-Transtrum-Qiu-Optimal experiment selection for parameter estimation in biological differential equation models
    We explore the question to what extent parameters can be efficiently estimated by appropriate experimental selection.
    experimental designsystems biologyAssociation & Data Fittingreaction ratesdecay rates
    Potential Scenario
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    1984-W_Brunner-D__Focht-Deterministic Three-Half-Order Kinetic Model for Microbial Degradation
    The kinetics of mineralization of carbonaceous substrates has been explained by a deterministic model which is applicable to either growth or nongrowth conditions in soil.
    kineticsnonlinear regressionsum of square errorsMonodlinearizemineralizationsubstratescarbonaceous
    Potential Scenario
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    2010-Roberto_Munoz-Alicea-Mathematical Model for Enzyme Kinetics-Multiple Timescales Analysis
    We study a basic model for enzyme substrate reaction. Through several assumptions and via nondimensionalization, we simplify the equations.
    kineticsEnzymesubstratenondimensionalizationmultiple timescales
    Article or Presentation
    190

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    70

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    2011-Brian_Winkel-Parameter_Estimates_in_Differential_Equation_Models_for_Chemical_Kinetics
    We estimate the parameters present in several differential equation models of chemical kinetics and logistic growth.
    kineticsparameter estimationlogisticchemical kineticschemical reaction
    Potential Scenario
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    40

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    1967-Israelsson- Johnsson-Circumnutations In Helianthus Annuus
    A theory is given for circumnutations in plants, especially hypocotyls of Helianthus annuus, which were used as experimental material.
    plantoscillationdelaycircumnutationturning
    Potential Scenario
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    2014-Vance-Eads-Sensitivity Analysis of a Three-Species Nonlinear Response Omnivory Model with Predator Stage Structure
    We investigate a three-species nonlinear response omnivory model incorporating stage structure in the top predator. The model consists of four coupled ordinary differential equations involving fourteen parameters.
    stage structuresensitivity analysismortalityomnivoreomnivory modelsearch rates
    Potential Scenario
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    2007-I-Liang_Chern-Mathematical Modeling and Differential Equations
    In this course, I will mainly focus on, but not limited to, two important classes of mathematical models by ordinary differential equations: • population dynamics in biology • dynamics in classical mechanics.
    population dynamicsecologydynamicsclassical mechanicschemical reaction
    Potential Scenario
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    2018-Banerjee-EtAl-Prey-Predator Model with a Nonlocal Bistable Dynamics of Prey
    The primary goal of our present work is to consider nonlocal consumption of resources in a spatiotemporal prey-predator model with bistable reaction kinetics for prey growth in the absence of predators.
    predator-preynonlocal consumptionTuring bifurcationspatial Hopf bifurcationspatio-temporal patternprey growth
    Potential Scenario
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    52

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    2004-Mitchell-von Meien-Krieger-Dalsenter-A review of recent developments in modeling of microbial growth kinetics
    Mathematical models are important tools for optimizing the design and operation of solid-state fermentation (SSF) bioreactors. Such models must describe the kinetics of microbial growth.
    Filamentous Fungisolid-state fermentationgrowth kineticsdiffusion-reactionoxygen transfer
    Potential Scenario
    156

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    88

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    2015-Heiko_Enderling-Integrating experimental data to calibrate quantitative cancer models
    For quantitative cancer models to be meaningful and interpretable the number of unknown parameters must be kept minimal. We focus on a tumor hierarchy of cancer stem and progenitor non-stem cancer cells.
    cancertumorfittingagent-based
    Modeling Scenario
    337

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    537

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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
    Potential Scenario
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    2014-Murillo-EtAl-Vertical Transmission in a Two-Strain Model of Dengue Fever
    The model is used to show that lower transmission rates of DENV-2 Asian are sufficient for displacing DENV-2 American in the presence of vertical transmission.
    Peruvector-host modeldengueepidemmiologyvertical transmission
    Potential Scenario
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    31

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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
    Modeling Scenario
    344

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    130

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    1-131-CaffeineElimination-ModelingScenario
    We model the concentration of caffeine 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.
    caffeineeliminationpharmacokineticsdrug
    Modeling Scenario
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    1-130-AspirinAbsorption-ModelingScenario
    We model the amount of aspirin absorbed by the human body at a constant rate. This is a ``zero-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
    pharmacokineticsdrugaspirin
    Potential Scenario
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    2010-Keesom-EtAl-Fishing for Answers Investigating Sustainable Harvesting Ra
    The purpose of this report is to determine and propose a model by which an optimal harvesting frequency can be determined to maintain a steady population of Alaskan salmon.
    fisheriesEuler's methodnonlinearlogistic harvestingcanabalismsalmon
    Potential Scenario
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    2023-TechShareNotes. Differential Equations Modeling
    TechShareNotes is a web site with rich differential equation modeling html pages and this one is about mixing in one, two, and three tanks, with interesting questions and problems as well as excellent diagrams and explanations.
    population dynamicspredator-preycircuitreactionspring masspharmacokineticscooling
    Potential Scenario
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    2017-Andras_Domokos-Differential Equations - Theory and Applications – Notes
    This is a terrific set of notes with models and applications woven into the material at every opportunity and data as well. This is introductory differential equations with attention to detail and motivation.
    Newton's Second Law of MotionNewton's Law of Coolingbiochemical reactionsPoiseuille’s Lawstopping distance
    Potential Scenario
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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