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    Potential Scenario
    130

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    2012-Yuan_Yuan-A coupled plankton system with instantaneous and delayed predation
    We present two simple plankton population models: one has instantaneous predation, another has delayed predation.
    phytoplanktonbifurcationorbitsherbivorous zooplanktoneffect of fishmaturation time delay
    Potential Scenario
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    56

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    2006-Cooke-Elderkin-Huang-Predator-Prey interactions with delays due to juvenile maturation
    This paper focuses on predator-prey models with juvenile/mature class structure for each of the predator and prey populations in turn, further classified by whether juvenile or mature individuals are active with respect to the predation process.
    predator-preyhost-parasitebifurcationage structrematuration delay
    Potential Scenario
    120

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    61

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    2014-Niemann-Miklos-Simple Method for Estimation of Parameters in First Order Systems
    A simple method for estimation of parameters in first order systems with time delays is presented in this paper.
    delaytime delystep response
    Potential Scenario
    769

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    73

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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
    238

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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
    258

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    88

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    2023-Roberto_Camassaa-Richard_McLaughlina-Tauberian identities and the connection to Wile E Coyote physics
    The application of the motion of a vertically suspended mass-spring system released under tension is studied focusing upon the delay timescale for the bottom mass as a function of the spring constants and masses.
    HangtimeTauberian IdentitiesRoad RunnerWile E. Coyote
    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
    Potential Scenario
    182

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    50

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    2012-Jambhekar-Breen-Extravascular Routes Of Drug Administration in Basic Pharamacokinetics
    This provides an excellent step-by-step of the physiology, construction of model, and notions like peak concentration as well as issues like lag time.
    concentrationphysiologydrugslag timeExtravascularPharamacokineticspeak time
    Potential Scenario
    205

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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
    199

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    57

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    2003-Yildirim-Mackey-Feedback Regulation in the Lactose Operon
    A mathematical model for the regulation of induction in the lac operon in Escherichia coli is presented.
    mRNAlactoselactose operonfeedback regulation
    Potential Scenario
    243

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    85

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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
    Article or Presentation
    129

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    33

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    2002-Patrick_Nelson-Alan_Perelson-Mathematical_analysis_of_delay_differential _equation_models_of_HIV-1_infection
    Models of HIV-1 infection that include intracellular delays are more accurate representations of the biology and change the estimated values of kinetic parameters when compared to models without delays.
    delayHIV-1T cellscombination antiviral therapy
    Modeling Scenario
    651

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    398

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    5-011-ModelingIbuprofren-ModelingScenario
    We consider modeling of data from a clinical experiment administered as oral doses of 400 mg ibuprofen, an analgesic pain reliever. Concentrations of ibuprofen in the serum/plasma of the subjects were recorded after the initial ingestion of the...
    dataAICAkaike Information Criterionabsorptionsum of square errorscompartment modelibuprofendelay
    Potential Scenario
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    89

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    2015-Jonathon_Easton, Jonathan-Mathematical models of health focusing on diabetes-Delay differential equations and data mining
    This is an exhaustive study with very good references of a linear system of four differential equations with and without delay to model diabetes in a human being.
    diabeteshealth model
    Potential Scenario
    198

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    65

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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
    134

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    62

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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
    129

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    40

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    2009-Marten-EtAl-Derivation and analysis of an ordinary differential equation for epilepsy dynamics
    In this paper we describe how an ordinary differential equation model of corticothalamic interactions may be obtained from a more general system of delay differential equations.
    delayepilepsy dynamicsepilepsybistabilityseizure activity
    Potential Scenario
    158

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    48

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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
    294

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    78

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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
    1603

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    60

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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