Tags: system

All Categories (1-20 of 113)

  1. 3-092-S-WirelessPower

    04 Aug 2021 | | Contributor(s):: Maila Hallare, Iordanka Panayotova

    This activity presents an engineering application that is modelled by a coupled system of two linear second-order differential equations with constant coefficients. One of the equations is homogeneous while the other one is non-homogeneous. The application is called wireless power transmission...

  2. 6-029-S-TumorGrowth

    04 Aug 2021 | | Contributor(s):: Allison Leigh Lewis

    This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of tumor growth over time. Students should have prior experience with solving ODEs using the separable...

  3. 6-017-S-OncolyticViruses

    03 Aug 2021 | | Contributor(s):: Iordanka Panayotova, Maila Hallare

    In this project, students explore oncolytic virotherapy using systems of differential equations and numerical simulations. The first activity guides the students in simulating the dynamics between the uninfected cancer cells x(t), the oncolytic virus-infected cancer cells y(t),  and the...

  4. 5-076-S-LanchesterLaws

    27 Jul 2021 | | Contributor(s):: Blain Patterson

    Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time, with the function depending only on A and B. In this project, you...

  5. 6-026-S-FakingGause

    30 Oct 2020 | | Contributor(s):: Brian Winkel

    We use a fake or toy data set to permit discovery of the parameters in a two population protozoan model used to study paramecium and yeast competiton in the 1930's studies of G.~F.~Gause in the Soviet Union.

  6. 5-010-S-DNADegradation

    21 Apr 2020 | | Contributor(s):: Brian Winkel

    We ask students to use the system of first order linear differential equations given in a source paper and estimates of the data from laboratory procedures from a plot to estimate the parameters and complete the modeling process. Then we seek to compare the results of the final model with...

  7. 6-045-S-CholeraTranmission

    19 Apr 2020 | | Contributor(s):: Urmi Ghosh-Dastidar

    A recent cholera outbreak in Haiti brought public attention to this disease. Cholera, a diarrheal disease, is caused by an intestinal bacterium, and if not addressed in a timely manner may become fatal. During the project described here, the students will learn how to solve and address a...

  8. 2019-Elishakoff, Isaac - Differential Equations of Love and Love of Differential Equations.

    06 Apr 2020 | | Contributor(s):: Brian Winkel

    Elishakoff, Isaac. 2019.   Differential Equations of Love and Love of Differential Equations. Journal of Humanistic Mathematics. 9(2): 1-22. See https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1549&context=jhm.SynopsisIn this paper, simple...

  9. 2018-Weber, Frank, Stefan Theers, Dirk Surmann, Uwe Ligges, and Claus Weihs - Sensitivity Analysis of Ordinary Differential Equation Models

    06 Apr 2020 | | Contributor(s):: Brian Winkel

    Weber, Frank, Stefan Theers, Dirk Surmann, Uwe Ligges, and Claus Weihs. 2018. Sensitivity Analysis of Ordinary Differential Equation Models.See https://d-nb.info/1160443556/34 .Introduction The goal of sensitivity analysis is to examine how sensitive a mathematical model...

  10. 2019-Selenne Bañuelos, Ty Danet, Cynthia Flores, and Angel Ramos -An Epidemiological Math Model Approach to a Political System with Three Parties. 

    05 Apr 2020 | | Contributor(s):: Brian Winkel

    Selenne Bañuelos, Ty Danet, Cynthia Flores, and Angel Ramos. 2019. An Epidemiological Math Model Approach to a Political System with Three Parties. CODEE Journal. Volume 12 Linking Differential Equations to Social Justice and Environmental Concerns Article...

  11. 2009-Marten, Frank, Serafim Rodrigues, Piotr Suffczynski, Mark P. Richardson, and John R. Terry - Derivation and analysis of an ordinary differential equation mean-field model for studying clinically recorded epilepsy dynamics.

    04 Apr 2020 | | Contributor(s):: Brian Winkel

    Marten, Frank, Serafim Rodrigues, Piotr Suffczynski, Mark P. Richardson, and John R. Terry. 2009. Derivation and analysis of an ordinary differential equation mean-field model for studying clinically recorded epilepsy dynamics. Phys. Rev. E 79,...

  12. 2012-Transtrum, Mark K and Peng Qiu - Optimal experiment selection for parameter estimation in biological differential equation models.

    02 Apr 2020 | | Contributor(s):: Brian Winkel

    Transtrum, Mark K and Peng Qiu. 2012. Optimal experiment selection for parameter estimation in biological differential equation models. Bioinformatics.  13(181): 1-12.See https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-13-181...

  13. 2018-Blomhøj, M. , T.H. Kjeldsen, and J. Ottesen. 2018. Compartment models. Lecture Notes.

    01 Apr 2020 | | Contributor(s):: Brian Winkel

    M. Blomhøj, T.H. Kjeldsen, and J. Ottesen. 2018. Compartment models. Lecture Notes 47 pp.    Chapter 1 - Compartment ModelsBackground: It is important to master the ability to develop models. Modeling of dynamical systems plays a very important role in...

  14. 1977-Freedman, H. I. and Paul Waltman - Mathematical models of population interactions with dispersal. I Stability of two habitats with and without a predator

    01 Apr 2020 | | Contributor(s):: Brian Winkel

    FREEDMAN, H. I. AND PAUL WALTMAN, 1977. MATHEMATICAL MODELS OF POPULATION INTERACTIONS WITHDISPERSAL. I: STABILITY OF TWO HABITATS WITH AND WITHOUTA PREDATOR.  SIAM J. APPL. MATH. 32(3): 631-648,See https://epubs.siam.org/doi/abs/10.1137/0132052?mobileUi=0&...

  15. 2007-Choisy, M., J.-F. Guégan, and P. Rohani -Mathematical Modeling of Infectious Diseases Dynamics.

    01 Apr 2020 | | Contributor(s):: Brian Winkel

    Choisy, M., J.-F. Guégan, and P. Rohani1. 2007. Mathematical Modeling of Infectious Diseases...

  16. 2011-Koch-Noble, G. A. - Drugs in the Classroom: Using Pharmacokinetics to Introduce Biomathematical Modeling

    29 Mar 2020 | | Contributor(s):: Brian Winkel

    Koch-Noble, G. A. 2011. Drugs in the Classroom: Using Pharmacokinetics to Introduce Biomathematical Modeling. Math. Model. Nat. Phenom. 6(6): 227-244.See https://www.mmnp-journal.org/articles/mmnp/pdf/2011/06/mmnp201166p227.pdf . Abstract: Pharmacokinetics is an excellent way to...

  17. 2018-Brinks, Ralph - Illness-Death Model in Chronic Disease Epidemiology: Characteristics of a Related, Differential Equation and an Inverse Problem.

    29 Mar 2020 | | Contributor(s):: Brian Winkel

    Brinks, Ralph. 2018. Illness-Death Model in Chronic Disease Epidemiology: Characteristics of a Related, Differential Equation and an Inverse Problem. Computational and Mathematical Methods in Medicine. Volume 2018, Article ID 5091096. 6...

  18. 2009-Noakes, Catherine J. and P. Andrew Sleigh - Mathematical models for assessing the role of airflow on the risk of airborne infection in hospital wards

    29 Mar 2020 | | Contributor(s):: Brian Winkel

    Noakes, Catherine J. and P. Andrew Sleigh. 2009. Mathematical models for assessing the role of airflow on the risk of airborne infection in hospital wards. J. R. Soc. Interface. 6: S791-S-800.See https://pubmed.ncbi.nlm.nih.gov/19812072/ .Abstract: Understanding the risk of...

  19. 2013-Pescitelli, Monica - Lotka Volterra Predator-Prey Model with a Predating Scavenger. Capstone project

    29 Mar 2020 | | Contributor(s):: Brian Winkel

    2013-Pescitelli-LotkaVolterraPredator-Prey-WithPredatingScavengerPescitelli, Monica. 2013. Lotka Volterra Predator-Prey Model with a Predating ScavengerAbstract: The classic Lotka Volterra equations are used to model the population dynamicsbetween two species: a predator and...

  20. 2017-Biswasa,  Haider Ali, Rajib Hossaina, and Mitun Kumar Mondala - Mathematical Modeling Applied to Sustainable Management of Marine Resources

    27 Mar 2020 | | Contributor(s):: Brian Winkel

    Biswasa,  Haider Ali, Rajib Hossaina, and Mitun Kumar Mondala. 2017. Mathematical Modeling Applied to Sustainable Management of Marine Resources. Procedia Engineering. 194: 337 – 344. Abstract: In this work, we formulate and study a nonlinear mathematical model of...