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    Potential Scenario
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    2010-Singh-Mishra-athematical modeling approach to study growth rate of grassroots technological innovations
    In this paper we have proposed a simple mathematical model by using ordinary differential equation to know the spread rate of technological innovations in rural India.
    logisticexponentialsigmoidtechnological innovationsasymptoticspread of innovation
    Modeling Scenario
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    1-165-FlushToilet-ModelingScenario
    This activity analyzes the spread of a technological innovation using the Bass Model from Economics. The equation is a first-order, two-parameter separable equation and the solution has a characteristic S-shaped curve or sigmoid curve.
    juliaDiffusioninnovationrate of innovationBass modelSolver
    Potential Scenario
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    2010-Kijek-Kijek-Modelling of Innovation Diffusion
    This paper offers a first order differential equation model for innovation diffusion, solves it, and offers qualitative analysis as well as approaches to estimating parameters with some data on final parameters for various countries.
    Bass modelinnovation diffusionLogistic modeldynamic model
    Potential Scenario
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    1989-EY_Rodin-K_Egan-Mathematics modelling of the rate of chemical reactions
    The development of improved designs for chemical reactors as well as the prediction of optimal operating conditions in chemical production are based on an understanding of the rates at which chemical processes occur.
    kineticsfirst orderreactionsecond orderzeroth order
    Potential Scenario
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    2012-Shargel-Yu-AccessPharmacy-Applied Biopharmaceutics and Pharmacokinetics
    Step by step formation of drug absorption models is shown with many good graphics of system and plots. Solutions are offered but no solution methods are shown.
    Michaelis-MentenEnzymesubstratecompartmentpharmacokineticsrate constanturinary dataabsorption rate
    Potential Scenario
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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
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    2009-Das-EtAl-Bioeconomic harvesting of a pre-predator fishery
    This paper deals with the problem of non-selective harvesting of a prey–predator system by using a reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis.
    predator-preyharvestingPontryagin’s maximum principlebioeconomicbionomic equilibriumbiotechnical productivitycatch-rate functionoptimal equilibrium
    Potential Scenario
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    2005-DieboldEtAl-Modeling Bond Yields In Finance And Macroeconomics
    From a macroeconomic perspective, the short-term interest rate is a policy instrument under the direct control of the central bank. From a finance perspective, long rates are risk-adjusted averages of expected future short rates.
    financeinterest ratebond yieldmacroeconomics
    Potential Scenario
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    73

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    2016-Erno_Keszei-Chemical Kinetics for Beginners
    The most important goal of kinetic research is the identification and characterisation of elementary molecular events which make possible the transformation of reactants into products.
    kineticszeroth order reactionfirst order reactionsecond order reactionreaction ratesthird order reaction
    Potential Scenario
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    70

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    2010-Del-Ciello-EtAl-Modeling Disease
    We model the transmission of a disease through a population. Such modeling is very important to the study of epidemiology and the practice of medicine.
    diseasespreadcarriessymptomaticasymptomatic
    Potential Scenario
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    1972-Suresh_Sethi-Optimal Control of the Vidale-Wolfe Advertising Model
    This paper considers an optimal-control problem for the dynamics of the Vidale-Wolfe advertising model, the optimal control being the rate of advertising expenditure to achieve a terminal market share within specified limits.
    Optimal Control Theoryadvertisingsales
    Potential Scenario
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    39

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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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    2018-Franklin_Chen-Teaching Kinetics through Differential Equations Constructed with a Berkeley MadonnaTM Flow Chart Model
    This kinetics manual has been successfully implemented in Physical Chemistry at UW-Green Bay in the fall semester of 2017, with the students’ success rate greater than 80%.
    kineticsPhysical ChemistryLotka Volterra equationsBerkeley Madonna platform
    Potential Scenario
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    2012-Lensyl-Urbano-The Draining of a Plastic Bottle-Integrating a Physics Experiment into Calculus
    I punched a small hole (about 1mm radius) in a one gallon plastic bottle and had my students measure the rate at which water drained.
    in-class activityexperimentTorricelli's Lawcylinder of waterexpderiment
    Potential Scenario
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    2004-Hill-Lozowski-Sampson-Experiments on ice spikes and a simple growth model
    We observed ice-spike growth using time-lapse digital photography, using two water types in two different containers.
    iceice spikebulk heat transfermass conservation
    Potential Scenario
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    2017-Bruce_Emerson-Wonderful World of Differential Equations
    This is a terrific set of noted 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 CoolingreactionsPoiseuille’s Lawstopping distancerate of changeproblemsmodeling opportunities
    Modeling Scenario
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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
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    1992-Emelie_Kenney-Differential equations and the AIDS epidemic
    This paper describes a lecture for Calculus II students in which the Acquired Immune Deficiency Syndrome was used to motivate study of first-order linear differential equations and the derivative as a rate of change.
    epidemicCDCAIDSDisease Control
    Potential Scenario
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    2015-Sivakumar-EtAl-Approximate Analytical Expression of Concentrations in a Kinetic Model for Biogas Generation from Banana Waste
    The initial value problem in a kinetic model for biogas generation from banana waste is discussed. The model involves the system of non-linear differential equations which has variety of non-linear rate function.
    chemical kineticsMichaelis-Menten kineticsanaerobic digestionacidogenic stepsbananamethanogenic stepswastes
    Potential Scenario
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    2005-Minna_Wedenberg-Pharmacokinetic modeling of gastric emptying
    The development of new drug substances is a complex, time consuming and expensive process. Reducing the time for drug development and avoiding late termination of candidate drugs are important challenges for the pharmaceutical industry.
    paracetamolpharmacokineticsstomachsmall intestinesulfapyridine