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    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
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    2011-W_Wood-Squigonometry
    The differential equations used to define a unit circle, namely x’(t) = - y(t), y’(t) = x(t), x(0) = 1, y(0) = 0 are generalized to produce interesting functions which satisfy trig like identities.
    TrigonometryTrigonometric Functionsparametric equationscirclesinecosinesquigonometryinverse function
    Potential Scenario
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    33

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    2011-Teleken-EtAl-Mathematical modeling of microbial growth in milk
    A mathematical model to predict microbial growth in milk was developed and analyzed. The model consists of a system of two differential equations of first order. The equations are based on physical hypotheses of population growth.
    bacteriadairymilkfood safetymicrobilogy
    Potential Scenario
    182

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    48

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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
    101

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    34

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    2011-Nguyen-Shi-Modeling the absorption circulation and metabolism of tirapazamine
    This apparently is a student project and it develops the kinetic model, uses Matlab for numerical solution, analytic solution and numerical solution.
    absorptionMichaelis-MentenMetabolismdrug metabolismcirculation
    Potential Scenario
    117

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    2011-Nancy_Rodrıguez-Applied Partial Differential Equations in Crime Modeling and Biological Aggregation
    In the first part we study a fully-parabolic system of PDEs for residential burglary ‘hotspots’ (spatio-temporal areas of high density of crime). In this work we are concerned with the existence and uniqueness of solutions of this model. In
    biologyDiffusionKeller-Segel modelchemotaxiscrime
    Potential Scenario
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    57

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    2011-Nakul-Chitnis-Introduction to Mathematical Epidemiology - Deterministic Compartmental Model
    Deterministic compartmental models form the simplest models in the mathematical study of infectious disease dynamics. They assume that a population is homogenous (all people are the same) and the only distinction is in their disease state.
    sensitivitydiseaseinfectionthresholdcompartmentbifrucation
    Potential Scenario
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    2011-Mandal-EtAl-Mathematical models of malaria
    The first aim of this article is to develop, starting from the basic models, a hierarchical structure of a range of deterministic models of different levels of complexity. The second is to elaborate, using some of the representative mathematical...
    epidemiologytransmissionhost-parasitemalariaRoss model
    Potential Scenario
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    46

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    2011-Lucas_Pulley-Analyzing Predator-Prey Models Using Systems of Ordinary Linear Differential Equations
    This research focused on applying biological mathematics to analyzing predation relationships, especially the relationship between the Canadian Lynx and the Snowshoe Hare.
    simulationpredator-preyLotka-VolterrapopulationCanadian LynxSnowshoe Harecritical values
    Potential Scenario
    113

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    34

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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
    110

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    43

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    2011-Kenny_Harwood-Modeling a RLC Circuit Current with Differential Equations
    This paper gives an abbreviated description of the photovaltaic effect (solar power production process) and then a RLC circuit will be modeled that is powered by a photovaltaic panel.
    tuningfrequency responseLC circuitRLC
    Potential Scenario
    105

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    38

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    2011-Gaff-Lenhart-Use of optimal control models to predict treatment time for managing tick-borne disease
    Tick-borne diseases have been on the rise recently, and correspondingly, there is an increased interest in implementing control measures to decrease the risk. Optimal control provides an ideal tool to identify the best method for reducing risk.
    diseaseoptimal controlTICKtick modeehrlichiosisbang bang control
    Potential Scenario
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    34

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    2011-GA_Koch-Noble-Drugs in the Classroom Using Pharmacokinetics to Introduce Biomathematical Modeling
    By beginning with simple model involving the half-life of a drug, students take advantage of their mathematical abilities to explore the biology.
    Biomathematicspharmacokinetics
    Potential Scenario
    123

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    36

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    2011-Cruz-Aponte-Herrera-Valdez-Mitigating effects of vaccination on influenza outbreaks given constraints in stockpile size and daily administrati
    We present a SIR-like model that explicitly takes into account vaccine supply and the number of vaccines administered per day and places data-informed limits on these parameters.
    vaccinationinfectionSIRepidemic
    Potential Scenario
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    34

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    2011-Carl_Leinbach-Beyond Newton's law of cooling - estimation of time since death
    The paper offers an excellent history of temperature-based methods and then proceeds to demonstrate these with some data. Here the history is rich and will support student investigation as well as faculty development.
    time of deathNewton's aw of cooling
    Potential Scenario
    140

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    33

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    2011-Brian_Winkel-Parameter Estimates in Differential Equation Models for Population Growth
    We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and multiple species competition models.
    logisticpopulationparameciaGausegradient search
    Potential Scenario
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    34

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    2010-Soetaert-EtAl-Solving Differential Equations in Rd SIMIODE Draft (5)
    Here we give a brief overview of differential equations that can now be solved by R.
    solving
    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
    Potential Scenario
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    35

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    2010-Shianga-EtAl-Computational model of the human glucose-insulin regulatory system
    A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced. The
    glucose tolerance testsum of squared residualsmultiple shooting methodcost function
    Potential Scenario
    166

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    37

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    2010-Shaza_Hussein-Predator-Prey Modeling
    The objective of this project was to create five projections of animal populations based on a simple predator-prey model and explore the trends visible.
    population dynamicspredator-preylogistic equationEndangered Catsdecreasing populationrabbitsfoxes