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    Potential Scenario
    111

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    29

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    2008-Jai-Li-Differential equations models for interacting wild and transgenic mosquito populations
    We formulate and study continuous-time models, based on systems of ordinary differential equations, for interacting wild and transgenic mosquito populations.
    Mosquito borne diseasespopulationsHolling-II-type mating ratestransgenic mosquitoesnonhyperbolic equilibriummosquitoes
    Potential Scenario
    154

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    75

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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
    Modeling Scenario
    408

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    279

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    1-024-MalariaControl-ModelingScenario
    This project offers students a chance to make policy recommendations based on the analysis of models using both linear (exponential decay) and non-linear (logistic growth) differential equations.
    population dynamicsmalariaPolicyDecision-makingEuler's methodpharmacokineticsmosquitoimproved Euler's methodHuen's methodUS Army
    Potential Scenario
    229

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    57

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    2009-Schaffer-Bronnikova-Controlling malaria
    The present paper reviews potential control strategies from the viewpoint of mathematical epidemiology.
    epidemiologymalariabifurcationmosquitotransgenic mosquitoes
    Potential Scenario
    140

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    55

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    2016-Lewnard-Townsend-Climatic and evolutionary drivers of phase shifts in the plague epidemics of colonial India
    Our analysis shows that historical datasets can yield powerful insights into the transmission dynamics of reemerging disease agents with which we have limited contemporary experience to guide quantitative modeling and inference.
    infectious diseasepVector-Borne Diseaselagueplague
    Potential Scenario
    126

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    57

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    2007-Choisy-Guégan-Rohani-Mathematical Modeling of Infectious Diseases Dynamics
    After presenting general notions of mathematical modeling (Section 22.2) and the nature of epidemiological data available to the modeler (Section 22.3), we detail the very basic SIR epidemiological model (Section 22.5).
    stochasticSIR modeldeterministicincubationinfectives
    Potential Scenario
    147

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    44

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    2006-Ousmane_Mousa_Tessa-Mathematical model for control of measles by vaccination
    In this article, we use a compartmental mathematical model of the dynamics of measles spread within a population with variable size to provide this framework.
    vaccinationcompartmentherd immunitymeaslesoptimal strategy
    Potential Scenario
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    55

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    2008-Abramson-Mathematical modeling of the spread of infectious diseases
    These are informal notes, mostly based on the bibliography listed at the end and on recent papers in the field. The practical use of these models is based on the fact that they can be kept realistic enough.
    infectious diseasebibliographyepidemiccowpoxsmallpoxcomplex networksspread disease
    Potential Scenario
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    72

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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
    134

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    46

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    0

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    2008-Abramson-Mathematical modeling of the spread of infectious diseases
    These are informal notes, mostly based on the bibliography listed at the end and on recent papers in the field. The practical use of these models is based on the fact that they can be kept realistic enough.
    infectious diseaseepidemiccowpoxsmallpoxcomplex networks
    Potential Scenario
    299

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    85

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    0

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    2018-Meredith_Greer-Ella_Livesay-Mathematical Epidemiology Goes to College
    In this article we present models that were inspired by two real-life outbreaks at a small residential college campus: H1N1 influenza in 2009 and, surprisingly, mumps in 2016.
    epidemiologydiseaseH1N1Influenzaoutbreak
    Potential Scenario
    221

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    105

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    2016-Lofgren-EtAl-Equations of the End Teaching Mathematical Modeling Using the Zombie Apocalypse
    In this article, we explore several uses of zombie epidemics to make mathematical modeling and infectious disease epidemiology more accessible to public health professionals, students, and the general public.
    simulationinfectious diseasediseaseepidemicZombieWhite Zed
    Modeling Scenario
    372

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    644

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    6-007-FunctionsAndDerivativesInSIRModels-ModelingScenario
    Given a system of differential equations, how do the solution graphs compare with the graphs of the differential equations? Students tackle this question using SIR models for well-known infectious diseases.
    epidemiologyspecies interactionsderivativesvisualizationinfectionSIR modelsLaw of Mass Action
    Potential Scenario
    224

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    74

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    2018-Arden_Baxter-Modeling Public Opinion
    In this paper, we adapt the epidemiological models to model the dynamics of public opinion. Public opinion is any view prevalent among the general public. Our model considers any topic or issue in which the public has two decisive and opposing...
    epidemiologypopulationpublic opinion
    Potential Scenario
    144

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    85

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    2014-Wrona-EtAl-Two-compartment model as a teaching tool for cholesterol homeostasis
    To investigate cholesterol transport in the circulatory system, we have previously developed a two-compartment mathematical model. Here, we show how this model can be used as a teaching tool for cholesterol homeostasis.
    metabolic syndromecompartment modelcholesterolhigh blood cholesterol
    Potential Scenario
    147

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    57

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    2017-Bonin-EtAl-Mathematical modeling based on ordinary differential equations - promising approach to vaccinology
    As a proof of concept, we developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature.
    immune systemyellow fevercomputational immunologycomputational vaccinology
    Potential Scenario
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    82

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    2016-Bonin-EtAl-Mathematical modeling based on ordinary differential equations-vaccinology
    We developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature.
    Immunologyimmune systemAntigenvaccinologyyellow fever
    Potential Scenario
    130

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    74

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    2015-Wrona-EtAl-Two-compartment model as a teaching tool for cholesterol homeostasis
    To investigate cholesterol transport in the circulatory system, we have previously developed a two-compartment mathematical model. Here, we show how this model can be used as a teaching tool for cholesterol homeostasis
    metabolic syndromecholesterolhigh blood cholesterolcholesterol homeostasis
    Potential Scenario
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    90

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    2014-Hrydziuszko-EtAl-Mathematical Two-compartment Model of Human Cholesterol Transport
    We develop a two-compartment mathematical model to investigate cholesterol transport in the circulatory system and its de novo synthesis in the liver.
    metabolic syndromecompartmentcholesteroltwo-compartment modelcholesterol transport
    Potential Scenario
    153

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    51

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    2012-Tweedle-Smith-Mathematical model of Bieber Fever-The most infectious disease of our time
    We develop a mathematical model to describe the spread of Bieber Fever, whereby individuals can be susceptible, Bieber-infected or bored of Bieber.
    infectious diseasediseaseinfectionmediaJustin BieberBieber feversymptomsboredreproductive ratio