
3092SWirelessPower
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 secondorder differential equations with constant coefficients. One of the equations is homogeneous while the other one is nonhomogeneous. The application is called wireless power transmission...

6029STumorGrowth
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...

6017SOncolyticViruses
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 virusinfected cancer cells y(t), and the...

5076SLanchesterLaws
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...

6026SFakingGause
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.

5010SDNADegradation
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...

6045SCholeraTranmission
19 Apr 2020   Contributor(s):: Urmi GhoshDastidar
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...

2019Elishakoff, 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): 122. See https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1549&context=jhm.SynopsisIn this paper, simple...

2018Weber, 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://dnb.info/1160443556/34 .Introduction The goal of sensitivity analysis is to examine how sensitive a mathematical model...

2019Selenne 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...

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

2012Transtrum, 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): 112.See https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471210513181...

2018Blomhøj, 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...

1977Freedman, 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): 631648,See https://epubs.siam.org/doi/abs/10.1137/0132052?mobileUi=0&...

2007Choisy, 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...

2011KochNoble, G. A.  Drugs in the Classroom: Using Pharmacokinetics to Introduce Biomathematical Modeling
29 Mar 2020   Contributor(s):: Brian Winkel
KochNoble, G. A. 2011. Drugs in the Classroom: Using Pharmacokinetics to Introduce Biomathematical Modeling. Math. Model. Nat. Phenom. 6(6): 227244.See https://www.mmnpjournal.org/articles/mmnp/pdf/2011/06/mmnp201166p227.pdf . Abstract: Pharmacokinetics is an excellent way to...

2018Brinks, Ralph  IllnessDeath 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. IllnessDeath 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...

2009Noakes, 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: S791S800.See https://pubmed.ncbi.nlm.nih.gov/19812072/ .Abstract: Understanding the risk of...

2013Pescitelli, Monica  Lotka Volterra PredatorPrey Model with a Predating Scavenger. Capstone project
29 Mar 2020   Contributor(s):: Brian Winkel
2013PescitelliLotkaVolterraPredatorPreyWithPredatingScavengerPescitelli, Monica. 2013. Lotka Volterra PredatorPrey Model with a Predating ScavengerAbstract: The classic Lotka Volterra equations are used to model the population dynamicsbetween two species: a predator and...

2017Biswasa, 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...