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    Potential Scenario
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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
    Potential Scenario
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    2008-Yang-EtAl-Differential Equation Model of HIV Infection of CD T-Cells with Delay 
    Abstract: An epidemic model of HIV infection of CD4+ T-cells with cure rate and delay is studied. We include a baseline ODE version of the model, and a differential-delay model with a discrete time delay.
    virusT cellsHopf bifurcationendemic equilibrium
    Potential Scenario
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    57

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    2011-Radouane_Yafia-A Study of Differential Equations Modeling Malignant Tumor Cells in Competition with Immune System
    In this paper, we present a competition model of malignant tumor growth that includes the immune system response. The model considers two populations: immune system (effector cells) and population of tumor (tumor cells).
    Immunologytumorhopf bifrucation
    Potential Scenario
    173

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    69

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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
    Potential Scenario
    161

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    46

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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
    Potential Scenario
    147

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    57

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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
    161

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    82

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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
    Potential Scenario
    146

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    40

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    2012-José_Sérgio_Domingues-Gompertz Model - Resolution and Analysis for Tumors
    The main objective of this paper is to use the Gompertz equation in order to study the development of blood irrigated solid tumors, using parameters defined in some important bibliographic references about the mathematical modelling of tumors.
    tumorGompertz equationgrowth tumor
    Potential Scenario
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    1977-Michael_Mackey-Leon_Glass-Oscillation and Chaos in Physiological Control Systems
    First-order nonlinear differential-delay equations describing physiological control systems are studied. The equations display a broad diversity of dynamical behavior including limit cycle oscillation.
    sensitivitychaosparametersRespirationdelayblood cells
    Potential Scenario
    294

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    47

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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
    155

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    87

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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
    140

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    65

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    2017-Allali-EtAl-Mathematical Modeling of the Adaptive Immune Responses in the Early Stage of the HBV Infection
    The aim of this paper is to study the early stage of HBV infection and impact delay in the infection process on the adaptive immune response, which includes cytotoxic T-lymphocytes and antibodies.
    logisticHBV infectionadaptive immunie responseT-lymphocytes
    Potential Scenario
    144

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    2014-Wrona-EtAl-Two-compartment model as a teaching tool for cholesterol homeostasis
    To investigate cholesterol transport in the circulatory system, we have previously developed a two-compartment mathematical model. Here, we show how this model can be used as a teaching tool for cholesterol homeostasis.
    metabolic syndromecompartment modelcholesterolhigh blood cholesterol
    Potential Scenario
    130

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    2015-Wrona-EtAl-Two-compartment model as a teaching tool for cholesterol homeostasis
    To investigate cholesterol transport in the circulatory system, we have previously developed a two-compartment mathematical model. Here, we show how this model can be used as a teaching tool for cholesterol homeostasis
    metabolic syndromecholesterolhigh blood cholesterolcholesterol homeostasis