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    6-005-InsectColonySurvivalOpt-ModelingScenario
    We present a system of nonlinear differential equations to model the control of energy flow into producing workers or reproducers in an insect colony, using a set of given parameters and a number...

    Keywords: optimizationOptimal Control Theoryinsect colonyoptimal controlnatural resourcesPointryagin's Maximum Principlecontrol variable

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    2017-Justin_Krueger-Parameter Estimation Methods for Ordinary Differential Equation Models with Applications to Microbiology
    We demonstrate the feasibility of principal differential analysis using simulation studies and then apply the method to intestinal and vaginal microbiota data.

    Keywords: microbiologyLotka Volterrramicrobiota

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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...

    Keywords: metabolic syndromecompartment modelcholesterolhigh blood cholesterol

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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...

    Keywords: infectious diseasepVector-Borne Diseaselagueplague

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    2014-Wang-EtAl-Estimating Mixed-Effects Differential Equation Models
    When multiple replicates of measurements are available for the dynamic process, it is of great interest to estimate mixed-effects in the ODE model for the process. We propose a semiparametric...

    Keywords: pharmacokineticsdynamic modelssmoothingsplinemixed-effects modelsHiV combination therapy

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

    Keywords: epidemiologymalariabifurcationmosquitotransgenic mosquitoes

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    2009-Munz-EtAl-When Zombies Attack-Mathematical modelling of an Outbreak of Zombie Infection
    We introduce a basic model for zombie infection, determine equilibria and their stability, and illustrate the outcome with numerical solutions.

    Keywords: zombiesinfectionepidemicwater treatmentlatent infectionquarantineimpulsive eradication

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    2006-Wilensky-Reisman-Thinking Like a Wolf a Sheep or a Firefly
    We describe a computation-based approach that enables students to investigate the connections between different biological levels using agent-based, embodied modeling tools.

    Keywords: simulationNetLogopredator-preyagent-basedwolffox

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    2006-Loyd-Wodarz-Drug Resistance in Acute Viral Infections-Rhinovirus as a Case Study
    We develop an epidemiological model that can be used to address the spread of resistance at the population level, and a virus dynamics model that can be used to study the dynamics of virus over the...

    Keywords: stabilityresistancevirusdrugepidemic competitionimmune responserhinovirus

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    1999-Khorasheh-Ahmadi-Gerayeli-Application of Direct Search Optimization for Pharmacokinetic Parameter Estimation
    For simple pharmacokinetic compartmental models, analytical solution to the governing differential equations provide a mean to evaluate the associated rate constants. Such methods, however, can not...

    Keywords: sum of square errorsleast squarespharmacokineticslineteicscompartmental modelsdirect search

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    1989-R_Blickhan-Spring Mass Model For Running-Hopping
    A simple spring—mass model consisting of a massless spring attached to a point mass describes the interdependency of mechanical parameters characterizing running and hopping of humans as a function...

    Keywords: spring massjumpjumping

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    1976-JG-Wagner-Computers in pharmacokinetics
    This is a seminal paper in pharmacokinetics in which the author introduces historic notions and approaches. As can be seen from the abstract there is a variety of material here.

    Keywords: kineticscomputerparametersPharmacologydrugspharmacokinetics

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    2018-Robert_Phair-Differential_equation_methods_for_simulation_of_GFP_kinetics_in_non–steady_state_experiments
    Here, we derive new tracer kinetic analytical methods for non–steady state biological systems by constructing mechanistic nonlinear differential equation models of the underlying cell biological...

    Keywords: protein quality controlkineticsCellssteady statechemical kineticsfluouresencephotoactivationinytracellular

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    2017-Thomas_Judson-The_Ordinary_Differential_Equations_Project
    This text is intended for a one-semester undergraduate course in ordinary differential equations. There are additional exercises or computer projects at the ends of many of the chapters.

    Keywords: projectsmathematical modeltextbooktechniquesfreeproofssageTheory

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    Venom Diversity & Evolution in Reptiles and Amphibians - An education module for university students
    This module contains information for a three part series introducing the venom system in reptiles and discussing it in an evolutionary context. In the first part venom and its ecological roles are...

    Keywords: geneticsEvolutionecologyHerpetologyAmphibans and ReptilesVenom

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    1-009-Bifurcation-TechniqueNarrative
    We lead students to investigate first-order differential equations that contain unknown parameters. Students discover what happens to the qualitative behavior of solutions to these equations as...

    Keywords: bifurcationqualitative behaviorbifurcation diagram

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    1-190-IntroClass-ModelingScenario
    Students go through development of ideas in mathematical modeling with differential equations. They encounter fundamental ideas of unlimited population growth, limited population growth and a...

    Keywords: population dynamicspredator-preylogisticexponentialgraphical interpretationsqualitative analysis

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    3-001-SpringMassDataAnalysis-ModelingScenario
    We offer data on position of a mass at end of spring over time where the spring mass configuration has damping due to taped flat index cards at the bottom of the mass. Modeling of a spring mass...

    Keywords: datadampingspring-mass systemNewton's Second Law of Motionspring constantHooke's Law

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    5-040-TunedMassDampers-PartII-ModelingScenario
    Studentsbuild mathematical models to mitigate dangerous swaying in structures using structural improvements called Tuned Mass Dampers (TMD). We model the motion of the original structure as a...

    Keywords: structureresistancespring-mass-dashpotearthquakevibrationcontroldampingtuned mass damperstiffnessreduction of vibration

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    6-012-RiverCrossing-ModelingScenario
    Students develop a model of a river crossing in a boat with thrust using Newton's Second Law of Motion from a Free Body Diagram they construct. The model is thence a system of one second order...

    Keywords: dragonNewton's Second Law of Motionriver crossinriver currentvelocity profilethrustFree Body Diagram

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