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    Potential Scenario
    146

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    54

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    2008-Ratneesh_Suri-Optimal harvesting strategies for fisheries-differential equations approach
    We develop and investigate the harvesting model in both deterministic and stochastic settings. We first employ the Expected Net Present Value approach and determine optimal harvesting policy using various optimization techniques including optimal...
    optimal controlsustainable yieldmaximum sustainable yieldharvestExpected Net Present Valuecalculus of variationsdynamic programmingmaximum economic yield
    Potential Scenario
    181

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    69

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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
    154

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    62

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    2007-Mogen_Steffensen-Differential Equations in Finance and Life Insurance
    The mathematics of finance and the mathematics of life insurance were always intersecting. Life insurance contracts specify an exchange of streams of payments between the insurance company and the contract holder.
    financedisabilitylife insurancemortalityinsuraneThiele’s equationBlack-Scholes equation
    Potential Scenario
    177

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    58

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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
    143

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    24

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    2008-Duran-Caginalp-Parameter optimization for differential equations in asset price forecasting
    The optimization procedure is used in conjunction with daily market prices (MPs) and net asset values to determine the parameters for which the AFDE yield the best fit for the previous n days.
    financeinverse problemnumerical nonlinear optimizationasset flowfinancial market dynamicsmarket return prediction algorithm
    Article or Presentation
    173

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    52

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    2010-Kar-Chakraborty-Bioeconomic_modelling_of_a_prey_predator_system_using_differential_algebraic_equations
    We propose a biological economic model based on prey-predator dynamics where the prey species are continuously harvested and predation is considered with type II functional response.
    economicsbifurcationharvestfisheryequilibriumdifferential algebraic equation
    Modeling Scenario
    314

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    216

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    1-003-CollegeSavings-ModelingScenario
    We present a modeling opportunity for students in which they have to plan and model for saving for a child's complete college education.
    collegesavingsinterest ratecollege costsensitiviyty
    Potential Scenario
    432

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    86

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    2020-Cline-EtAl-A Vision for Projects Across the Mathematics Curriculum
    We describe a model that incorporates projects at all stages across the undergraduate mathematics curriculum. Finally, we provide samples of projects that we have used in selected courses.
    projectstechnical writinginterdisciplinary skills
    Potential Scenario
    161

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    69

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    1972-R_C_Rothermel-A Mathematical Model for Predicting Fire Spread in Wildland Fuels
    The development of a mathematical model for predicting rate of fire spread and intensity applicable to a wide range of wildland fuels is presented from the conceptual stage through evaluation and demonstration of results to hypothetical fuel models.
    predictionforest firefire managementfire spreadfuel
    Potential Scenario
    184

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    45

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    1991-Thoddi_Kotiah-Difference and differential equations in the mathematics of finance
    Many problems arising in the mathematics of finance involve identical money flows at regular time intervals and are typically solved by appropriate valuation at a focal date or by setting up an equation of value.
    financesavingsgrowth fundinterestmortgageannuitydepreciation
    Modeling Scenario
    301

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    135

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    1-118-SolowEconomicGrowth-ModelingScenario
    Students construct and analyze the celebrated Solow-Swan model of economic growth theory. The project is divided into three sequential parts to teach students to understand, develop, and analyze a simple nonlinear model of economic dynamics.
    optimizationeconomicssteady stategrowthSolow-Swan modelcapitalproductionlaborGolden Rule of Economic Growth
    Potential Scenario
    174

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    75

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    0

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    2012-Murray_Bourne-Modeling fish stocks
    Discusses many models of harvesting and consequences.
    fishlogisticmanagementsusustainable developmentharvestfish stockoverpopulatedunsustainable
    Potential Scenario
    155

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    95

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    2002-Ragnar-Norberg-Basic Life Insurance Mathematics
    Presents fundamentals of life insurance, mortality, savings, banks, finance, reserves, pensions, stochastic processes.
    financestochastic processessavingslife insurancebanksreservespensionsmortality
    Modeling Scenario
    221

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    130

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    1-009-ICUSpread-ModelingScenario
    We offer students the opportunity to model the percentage of voluntary nonprofit hospitals in the United States with Intensive Care Units during the period of 1958-1974.
    logisticsum of square errorsIntensive Care Unithospitalspread
    Modeling Scenario
    307

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    148

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    0

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    1-119-DairyFarming-ModelingScenario
    A simple first order population growth model is presented. The challenge is to produce a final differential equation which is the result of the difference or ratio of birth and death rates. This ratio is not immediately intuitive.
    population dynamicsdairyfarmers' marketsgrowthcow
    Potential Scenario
    162

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    75

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    2015-Joshi-EtAl-Optimal control of an SIR model with changing behavior through an education campaign
    We study stability analysis and use optimal control theory on the system of differential equations to achieve the goal of minimizing the infected population (while minimizing the cost).
    SIR modelsvaccinepopulationwater treatmentsusceptibleeducation campaignminimizing costinfected
    Potential Scenario
    131

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    61

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    2015-Erzo-Luttmer-Four Models of Knowledge Diffusion and Growth
    This paper describes how long-run growth emerges in four closely related models that combine individual discovery with some form of social learning.
    knowledge diffusionstationary distributionsproductivity distributionreaction-diffusion equationsquasi-stationary distributions
    Potential Scenario
    161

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    69

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    2014-Patel-Schlijper-Models of Consumer Behavior
    The problem posed to the Study Group was to construct models for consumer behaviour that might be useful in tools for brand management in markets for fast-moving consumer goods.
    consumer behaviormarket share
    Potential Scenario
    169

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    52

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    2012-Ogunrinde-Sunday-On some models based on second order differential equation
    This paper presents some models based on second order differential equations. Such models include interaction between different kinds of species in an environment and pricing policy for optimum inventory level of a firm.
    species interactionpricing policyoptimal inventory
    Potential Scenario
    149

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    45

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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