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    Potential Scenario
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    2004-Aldo_Rescigno-On the use of pharmacokinetic models
    In this paper I will define in a simple and logical way a set of useful pharmacokinetic parameters and show how their estimation depends on the assumed model.
    compartmentsteady statepharmacokineticsvolume distribution
    Potential Scenario
    294

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    2017-Suebcharoen-Analysis of a Predator-Prey Model with Switching and Stage-Structure for Predator
    This paper studies the behavior of a predator-prey model with switching and stage-structure for predator.
    stage structurepredatorpreybifurcationswitching
    Potential Scenario
    141

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    67

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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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    59

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    2017-Agmour-EtAl-Optimization of the Two Fishermen's Profits Exploiting Three Competing Species Where Prices Depend on Harvest
    The main purpose of this work is to define the fishing effort that maximizes the profit of each fisherman, but all of them have to respect two constraints: the first one is the sustainable management of the resources and the second one is...
    FishingharvestNash equilibriumoptimizeprofits
    Potential Scenario
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    90

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    1957-Axelrod_ Brady_Witkop_Evarts-The Distribution and Metabolism of Lysergic Acid Diethylamide
    The development of a specific and sensitive method for the estimation of LSD in biological materials has enabled us to study the tissue distribution, excretion, rate of biotransformation, and metabolism of the drug, as well as the subcellular...
    mathematical modeldataLSDMetabolismbloodstreamlysergic acid diethylamidedistribution
    Potential Scenario
    196

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    83

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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
    Potential Scenario
    143

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    59

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    2006-Han-EtAl-Ordinary differential equation models for ethanol pharmacokinetic based on anatomy and physiology
    Physiologically-based pharmacokinetic (PBPK) models have been used to describe the distribution and elimination characteristics of intravenous ethanol administration.
    liverwortsintraveneouspharmacokineticsethanolethanol infustionpharmacodynamictissue model
    Potential Scenario
    208

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    1971-Carl_Metzler-Usefulness Of Two Compartment Open Model In Pharmacokinetics
    Compartment models are widely used in pharmaceutical research to quantitate the kinetics of absorption, distribution, metabolism and excretion of a drug. In this article two applications of the two compartment open model are discussed.
    LSDcompartmentpharmacokinetics
    Potential Scenario
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    65

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    2013-Deboeck-Bergeman-The reservoir model-DE model of psychological regulation
    The following article describes a differential equation model based on the concept of a reservoir for psychological regulation.
    adaptive copingReservoirsNotre Dame Longitudinal Study on Agingoutputinput distributionstressorscoping resources
    Potential Scenario
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    57

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    1986-Istvan_Gyori-Connections between compartment systems pipes and integro-differential equations
    In this paper we give the mathematical description of models in which the mass transport between compartments requires a given definite time or transit times are distributed according to given probability distribution functions.
    physiologypipelinecompartmentbloodcirculationintegro-differential equation
    Potential Scenario
    281

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    70

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    1968-Wagner-Aghajanian-Bing-Correlation of performance test scores with tissue concentration of lysergic acid diethylamide
    This paper offers a two compartment model of lysergic acid diethylamide (LSD) in volunteer students and through parameter estimation models the amount of LSD in the tissue after its initial administration through the plasma.
    LSDcorrelation coefficientcompartment modellysergic acid diethylamideperformancetest scoretissue concentration
    Modeling Scenario
    333

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    123

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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
    Potential Scenario
    167

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    90

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    2018-Akman-EtAl-Parameter Estimation in Ordinary Differential Equations Modeling via Particle Swarm Optimization
    We demonstrate Particle Swarm Optimization efficacy by showing that it outstrips evolutionary computing methods previously used to analyze an epidemic model.
    epidemicParticle Swarm Optimizationoptimize parameters
    Potential Scenario
    158

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    52

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    2011-Kurt_Kreith-The Mathematics of Global Change
    The authors discuss broad issues and then focus on specifics like exponential growth, logistic growth, and the logistic equation with delay.
    exponential growthlogistic growth
    Potential Scenario
    139

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    90

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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
    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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    2011-Yanyu_Xiao-Study of Malaria Transmission Dynamics by Mathematical Models
    The novelty lies in the fact that different distribution functions are used to describe the variance of individual latencies. The theoretical results of this project indicate that latencies reduce the basic reproduction number.
    infectious diseaseinfectionmalarialatencyspatial dispersalmulti-species
    Potential Scenario
    254

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    91

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    2018-David_Bourne-Pharmacokinetics – Source Material
    This is a rich source of pharmacokinetics modeling activities and data. These are syllabus notes with homework assignments listed.
    boluspharmacokineticspharmacodynamicdrug distribution
    Modeling Scenario
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    5-001-LSD-ModelingScenario
    We describe the use of a two compartment model of a linear system of first order linear differential equations to model lysergic acid diethylamide (LSD) in the body. We provide the data from the literature.
    LSDSpanishcompartmentpharmacokineticslysergic acid diethylamide
    Modeling Scenario
    264

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    215

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    6-010-SocialCampaign-ModelingScenario
    The epidemic modeling problem is formulated as a system of three nonlinear, first order differential equations in which three compartments (S, I, and R) of the population are linked.
    diseasegrowth rateJudgment and Decision MakingSIR modelinfections diseasesocial campaignrecovery ratedelay timejoining processquitting processexponential distribution