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    Potential Scenario
    110

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    40

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    1989-EY_Rodin-S_Jaques-Countercurrent Oxygen Exchange in the Swim Bladders of Deep-Sea Fish
    Oxygen diffuses from lungs into blood, nutrients diffuse from intestinal tracts into blood and from blood into various cells, and waste products diffuse from cells back into blood.
    fishCell Membraneflowbloodbladdercountercurrent
    Modeling Scenario
    274

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    384

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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 effectiveness to deliver quality dialysis.
    countercurrent multiplierkidneydialysisconcurrentcompartment
    Potential Scenario
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    49

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    2018-Winkle-Igoshin-Bennett-Josic-Ott-Modeling_Mechanical_Interactions_in_Growing_Populations_of_Rod-Shaped_Bacteria
    Here, we present an agent-based model that allows growing cells to detect and respond to mechanical interactions.
    bacteriaagent-basedpopulationbrod-shapedcellular growth
    Potential Scenario
    146

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    37

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    2017-Helen-Byrne-Further Mathematics Biology
    These studies will be in the context of ecological, biological and biochemical applications.
    epidemicschemotaxisenzyme-substrateion channelsnerve pulsesgene proagationtumour
    Potential Scenario
    661

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    63

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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
    Article or Presentation
    456

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    80

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    2007-John_Jungck-Ten_Equations_that_Changed_Biology-Mathematics_in_Problem-Solving_Biology_Curricula The author
    These equations were selected upon the basis of wide-spread recognition of the value of the models.
    biologyequationsten equations
    Potential Scenario
    255

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    39

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    2018-Robert_Phair-Differential_equation_methods_for_simulation_of_GFP_kinetics_in_non–steady_state_experiments
    Here, we derive new tracer kinetic analytical methods for non–steady state biological systems by constructing mechanistic nonlinear differential equation models of the underlying cell biological processes.
    protein quality controlkineticsCellssteady statechemical kineticsfluouresencephotoactivationinytracellular
    Potential Scenario
    122

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    83

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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
    Potential Scenario
    114

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    51

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    2016-Barbarossa-Kuttler-Mathematical Modeling of Bacteria Communication in Continuous Cultures
    This paper presents a simple system of delay differential equations (DDEs) for quorum sensing of Pseudomonas putida with one positive feedback plus one (delayed) negative feedback mechanism.
    gene regulatory networkschemostatbifurcationNumerical Simulationquorum sensing
    Potential Scenario
    111

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    63

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    0

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    2015-Khan-EtAl-How differential equations influence the tumor growth via mathematical models
    This work demonstrates the importance of differential equations to develop mathematical model of tumor growth.
    tumorcancdercancerous cellsimmunotherapymalignant
    Free Online Textbook
    378

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    82

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    2012-Brian_Ingalls-Mathematical Modelling in Systems Biology An Introduction
    This is a comprehensive text with much biology background to motivate the mathematical modeling, exercises and answers, and many rich examples.
    spatialsensitivity analysisgene regulatory networksstochasticbifurcationmetabolic networkselectrophysiologytransductionrate lawsbiochemical reactions
    Potential Scenario
    126

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    47

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    2018-Dyjuan_Tatro-The_Mathematics_of_Cancer-Fitting_Gompertz_Equation_to_Tumor_Growth
    Fitting the Gompertz Model to long term breast cancer study data, this project ascertains gompertzian parameters that can be used to predicts tumor growth as a function of time.
    tumorgrowthGompertzfittingparameter
    Potential Scenario
    152

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    43

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    2002-Nelson-Perelson-Mathematical analysis of delay differential equations models of HIV-1 infection
    We develop and analyze a set of models that include intracellular delays, combination antiretroviral therapy, and the dynamics of both infected and uninfected T cells.
    infectionHIVT cells
    Modeling Scenario
    283

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    150

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    1-005B-ChemDataCollection-ModelingScenario
    A chemistry graduate student is collecting data on a chemical reaction and does a poor job of collecting the data. Indeed, he only collects the data at the start and end of a number of three minute intervals and does not note the times.
    kineticslaboratoryorder of reactionchemical reactionchemical datainfusion
    Potential Scenario
    119

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    42

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    2017-Bonin-EtAl-Mathematical modeling based on ordinary differential equations - promising approach to vaccinology
    As a proof of concept, 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.
    immune systemyellow fevercomputational immunologycomputational vaccinology
    Potential Scenario
    125

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    63

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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.
    Immunologyimmune systemAntigenvaccinologyyellow fever
    Article or Presentation
    194

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    42

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    2013-Brian_Winkel-Reflecting_On_Walls
    We reflect on our passion for teaching mathematics, useful mathematics, by considering our understandings of just what a wall is and what a wall means to us.
    mathematicsmathematical modellearningcell wall