SIMIODE: Resources

Modeling Scenario

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1-155-CruiseControl-ModelingScenario

In this project we illustrate the design of a proportional-integral-derivative (PID) cruise control algorithm for an automobile. PID control is one of the most common techniques in control engineering.

PID controllerfeedback controlControl theorycruise controlautomobileclosed-loop controlinput-ouputblock diagram

Potential Scenario

223

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2014-XM-Huang-Ordinary Differential Equation Model and its Application in the Prediction Control of Population

In this paper, we study two kinds of ordinary differential equation models, i.e., Malthus model and Logistic model, and discuss their applications in the prediction control of population.

population dynamicsLogistic modelMalthus ModelPopulation Prediction Control

Potential Scenario

180

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2017-Sim-EtAl-Optimal control of a coupled tanks system with model-reality differences

In this paper, an efficient computational approach is proposed to optimize and control a coupled tanks system.

optimal controlflowtankscoupled tanks

Modeling Scenario

392

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1-021-FeralCatControl-ModelingScenario

Students act as professional mathematical consultants and write a report analyzing the client's problem. The client company is a fictional organization which advocates for the use of trap-neuter-return (TNR) as a control method for feral cat...

population growthcontrolferal catspopulation controlneutertrap-killtrap-neuter-return

Potential Scenario

192

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2000-Idels-Wang-Harvesting Fisheries Management Strategies With Modified Effort Function

This study concludes that a control parameter beta (the magnitude of the effect of the fish population size on the fishing effort function E), changes not only the rate at which the population goes to equilibrium, but also the equilibrium values.

sustainabilityfishFishingmanagementharvestfisherstrategyoverfishing

Potential Scenario

202

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2017-Jean-Roux-Mathematical Models in Air Quality Problems

Presents many models with analysis in air quality control. Starts with chemical kinetics models and builds complexity to PDE models.

air pollution effects on forest ecosystemsfinite volume methodboundary layerchemical kineticsfinite differenceemissionsdepositionsadvection

Modeling Scenario

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7-011-CoupledSystemLaplace-ModelingScenario

Differential equations and Laplace transforms are an integral part of control problems in engineering systems. We consider a baby warming device.

transfer functionpolycarbonatebaby heatercoupled systemheating

Modeling Scenario

420

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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

Modeling Scenario

266

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266

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1-079-HomeHeating-ModelingScenario

This project concerns using Newton's Law of Cooling to model the heating of a house. In particular, if one is going away for awhile, is it more economical to leave a house at a desired temperature or reheat it upon return?

Optimal Control TheorytemperatureheatfurnaceNewton's Law of Coolinghome heatingspecific heat

Modeling Scenario

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1-089-SpreadOfDisease-ModelingScenario

In this project I want to use the algebra based concept “difference quotient” to solve differential equations models with the help of Excel. That means even students with only a College Algebra background, can still enjoy differential equation...

SIR modelProportionderivativedifference quotientSleeping Beautycontagious disease

Potential Scenario

201

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2015-Valerie_Billard-Pharmacokinetic-pharmacodynamic relationship of anesthetic drugs - from modeling to clinical use

The purpose of this short review is to describe the basis of pharmacokinetics and modeling, the concentration-effects relationship, and drug interactions modeling to offer to anesthesiologists and non-anesthesiologists an overview of the rules to...

anesthesiapharmacokineticspharmacodynamicanesthetic

Potential Scenario

160

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2016-Manheim-EtAl-Improving Decision Support for Infectious Disease Prevention and Control

This report describes decision-support tools, including models and nonmodeling approaches, that are relevant to infectious disease prevention, detection, and response and aligns these tools with real-world policy questions that the tools can help...

infectious diseaseecosystemepidemicmodel policy

Article or Presentation

133

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65

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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.

datafirst orderparameterAIDS

Modeling Scenario

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1-096-OP-AMP-Differentiator-ModelingScenario

The output waveform (function) of a operational amplifier type of differentiator circuit is determined analytically from the first order governing ordinary differential equation and compared with the data acquired from numerical model (using...

simulationMeasurementfeedbackMultisimcircuitvoltageoperational amplifiervalidationSPICE

Modeling Scenario

306

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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

Free Online Textbook

220

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2018-Eduardo-Sontag-Lecture_Notes_on_Mathematical_Systems_Biology

I am often asked if it is OK to use these notes in courses at other universities. The answer is “of course!” though I strongly suggest that a link to my website be provided, so that students can always access the current version.

biologytextbooksystemsdyanmical system

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1-155-CruiseControl-ModelingScenario

2014-XM-Huang-Ordinary Differential Equation Model and its Application in the Prediction Control of Population

2017-Sim-EtAl-Optimal control of a coupled tanks system with model-reality differences

1-021-FeralCatControl-ModelingScenario

2000-Idels-Wang-Harvesting Fisheries Management Strategies With Modified Effort Function

2017-Jean-Roux-Mathematical Models in Air Quality Problems

7-011-CoupledSystemLaplace-ModelingScenario

1-024-MalariaControl-ModelingScenario

1-079-HomeHeating-ModelingScenario

1-089-SpreadOfDisease-ModelingScenario

2015-Valerie_Billard-Pharmacokinetic-pharmacodynamic relationship of anesthetic drugs - from modeling to clinical use

2016-Manheim-EtAl-Improving Decision Support for Infectious Disease Prevention and Control

1992-Emelie_Kenney-Differential_equations_and_the_AIDS_epidemic

1-096-OP-AMP-Differentiator-ModelingScenario

1-165-FlushToilet-ModelingScenario

2018-Eduardo-Sontag-Lecture_Notes_on_Mathematical_Systems_Biology

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