Tags: system

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  1. 7-011-Text-S-CoupledSystemLaplace

    31 Mar 2019 | | Contributor(s):: Mitaxi Mehta

    Differential equations and Laplace transforms are an integral part of control problems in engineering systems. However a clear explanation of the relationship of Laplace transforms with the differential equation formalism is difficult to find for coupled differential equations. Here we describe...

  2. 2017-Bonin EtAl - Math Modeling Based on ODE for Vaccinology

    09 Dec 2018 | | Contributor(s):: Brian Winkel

    Bonin, C.R.B. Et al. 2017. Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology. Human Vaccines and Immunotherapy. 13(2): 484–489.Abtract: New contributions that aim to accelerate the development or to improve the efficacy and safety of...

  3. 6-024-S-DronePackageDelivery

    18 Sep 2018 | | Contributor(s):: Eric Stachura, Robert Krueger

    In this scenario, students will begin by carefully reading through the problem statement and uncovering which information is useful. Students will derive a system of differential equations which describe the flight path of a drone delivering a package. Techniques used to derive the analytical...

  4. 6-006-T-ZombieGameHvZ

    09 Sep 2018 | | Contributor(s):: Jue Wang

    Invented in 2005, Humans vs. Zombies, or HvZ, is a game of tag, predominantly played at US college campuses. In this activity, students use systems of non-linear differential equations to model the HvZ game. Standard SIR and SIRS models are introduced to guide students as they set up the...

  5. 6-003-S-SchoolFluEpidemic

    28 Aug 2018 | | Contributor(s):: Darrell Weldon Pepper

    We offer a model of the spread of flu in a school dormitory and are asked to find when the flu levels reach their peak and explain long term behavior of the spread of the flu.

  6. 1-108-S-PoissonProcess

    27 Aug 2018 | | Contributor(s):: Mehdi Hakim-Hashemi

    In this project students learn to derive the probability density function (pdf) of the Poisson distribution and the cumulative distribution (cdf) of the waiting time. They will use them to solve problems in stochastic processes.

  7. 6-007-S-FunctionsAndDerivativesInSIRModels

    12 Aug 2018 | | Contributor(s):: Meredith Greer

  8. 2017-Allali-MathModelingOfAdaptiveImmunieResponses-HBVInfection

    07 Mar 2018 | | Contributor(s):: Karam Allali, Adil Meskaf, Abdessamad Tridane

    Karam Allali, Adil Meskaf, and Abdessamad Tridane. 2018. Mathematical Modeling of the Adaptive Immune Responses in the Early Stage of the HBV Infection. International Journal of Differential Equations. Volume 2017, Article ID 6710575, 13 pagesThis is an open access article distributed under the...

  9. 2003-RasmussenKeynes-LinesOfEigenVectorsSolutionsToSytemsOfLinearDifferentialEquations

    03 Mar 2018 | | Contributor(s):: Chris Rasmussen, Michael Keynes

    Rasmussen, Chris and  Michael Keynes. 2003. Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations.  PRIMUS. 13(4): 308-320.Abstract: The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of...

  10. 2011-Gaff EtAl-OptimalControlManagementTickBorneDisease

    03 Mar 2018 | | Contributor(s):: Holly D. Gaff

    Gaff, Holly D., Elsa Schaefer, and Suzanne Lenhart. 2011. Use of optimal control models to predict treatment time for managing tick-borne disease. Journal of Biological Dynamics. 5(5): 517-530Abstract:  Tick-borne diseases have been on the rise recently, and correspondingly, there is an...

  11. 2009-Das EtAl BioeconomicHarvesting-JBioDynamics

    03 Mar 2018 | | Contributor(s):: Tapasi Das

    Das, Tapasi, R. N. Mukherjee, and K. S. Chaurhur. 2009. Bioeconomic harvesting of a pre-predator fishery. Journal of Biological Dynamics. 3(5): 447-462.Abstract: This paper deals with the problem of non-selective harvesting of a prey–predator system by using a reasonable catch-rate...

  12. 2005-Sprott-DynamicModelsOfHappiness

    28 Nov 2017 | | Contributor(s):: Brian Winkel

    Sprott, J. C. 2005. Dynamical Models of Happiness. Nonlinear Dynamics, Psychology, and Life Sciences. 9(1): 23-35.Abstract: A sequence of models for the time evolution of one’s happiness in response to external events is described. These models with added nonlinearities can produce stable...

  13. 2007-ZenkerEtAl-InverseProblemsInMathPhysiology

    28 Nov 2017 | | Contributor(s):: Brian Winkel

    Zenker S, J. Rubin, and G. Clermont. 2007. From inverse problems in mathematical physiology to quantitative differential diagnoses. PLoS Comput Biol.  3(11): e204.Abstract: The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in...

  14. 2016-LifgrenEtAl-EquationsOfTheEnd-MathModelingUsingZombieApocapylse

    28 Nov 2017 | | Contributor(s):: Brian Winkel

    Lofgren, Eric T., Kristy M. Collins, Tara C. Smith, and Reed A. Cartwright. 2016. Equations of the End: Teaching Mathematical Modeling Using the Zombie Apocalypse. Journal of Microbiology & Biology Education. 17(1): 137-142.From the Introduction, “Mathematical models of infectious...

  15. 2014-Easton-MathModelsOfHealthFocusingOnDiabetes-DelayDEAndDataMining

    28 Nov 2017 | | Contributor(s):: Brian Winkel

    Easton, Jonathan. 2015.  Mathematical models of health focusing on diabetes: Delay differential equations and data mining . PhD Thesis.  Northumbria University Newcastle. http://nrl.northumbria.ac.uk/23582/. Accessed 27 November 2017.Abstract: Mathematical models have been applied to...

  16. 1988-Strogatz-LoveAffairsAndDifferentialEquations

    26 Nov 2017 | | Contributor(s):: Brian Winkel

    Strogatz, Steven H. 1988. Love Affairs and Differential Equations. Mathematics Magazine. 61(7):  35.This is a system of differential equations to describe the love between Shakespeare’s Romeo and Juliet.Keywords: differential equation, system, linear, parameters 

  17. 2017-Adler-Mathematically Modeling Asthma-SIAM

    09 Oct 2017 | | Contributor(s):: Brian Winkel

    Adler, Fred. 2017 Mathematicslly Modeling Asthma. Blog Posting.  3 pp. https://sinews.siam.org/Details-Page/mathematically-modeling-asthma . Accessed 9 October 2017. From the article, “Asthma—like diabetes, heart disease, and cancer—does not have a single initiating cause,...

  18. Ramsay-From Data To Differential Equations

    23 Sep 2017 | | Contributor(s):: Brian Winkel

    Ramsay, Jim.  From Data To Differential Equations. Presentation. 52 slides.Themes:Differential equations are powerful tools for modeling data.There are new methods for estimating differential equations directly from data.Some examples are offered, drawn from chemical engineering and...

  19. 2011-CaoEtAl-Robust Estimation for Ordinary Differential Equation Models

    23 Sep 2017 | | Contributor(s):: Brian Winkel

    Cao, J., L. Wang, J. Xu. 2011. Robust estimation for ordinary differential equation models. Biometrics.  67(4): 1305-13.Abstract: Applied scientists often like to use ordinary differential equations (ODEs) to model complex dynamic processes that arise in biology, engineering, medicine and...

  20. 2009-Wilson-Differential Equation Models for Forecasting Highway Traffic Flow

    23 Sep 2017 | | Contributor(s):: Brian Winkel

    Wilson, R. Eddie. 2009. Differential Equation Models for Forecasting Highway Traffic FlowPresentation at Conference on Traffic Modelling. The Open University, Milton Keynes, UK. 31 March. 32 slides. This talk builds the mathematical model for traffic flow and addresses the issues of...