
5002TPhasePortraitForRelationshipDynamics
15 Aug 2019  Modeling Scenarios  Contributor(s): Brian Winkel
The different possible dynamics of a twoperson romantic relationship are modeled  as a linear two dimensional system of equations  and analyzed. Students are guided to explore how the mathematical model of one relationship type can be obtained by modifying the mathematical model of another....

7011TextTCoupledSystemLaplace
31 Mar 2019  Technique Narratives  Contributor(s): Brian Winkel
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...

7011TextSCoupledSystemLaplace
31 Mar 2019  Technique Narratives  Contributor(s): Brian Winkel
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...

2017Bonin EtAl  Math Modeling Based on ODE for Vaccinology
09 Dec 2018  Potential Scenario Ideas  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...

6024TDronePackageDelivery
18 Sep 2018  Modeling Scenarios  Contributor(s): Brian Winkel
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 first order differential equations which describe the flight path of a drone delivering a package. Techniques used to derive the...

6024SDronePackageDelivery
18 Sep 2018  Modeling Scenarios  Contributor(s): Brian Winkel
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...

6006TZombieGameHvZ
09 Sep 2018  Modeling Scenarios  Contributor(s): Brian Winkel
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 nonlinear differential equations to model the HvZ game. Standard SIR and SIRS models are introduced to guide students as they set up the...

6003TSchoolFluEpidemic
28 Aug 2018  Modeling Scenarios  Contributor(s): Brian Winkel
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.

6003SSchoolFluEpidemic
28 Aug 2018  Modeling Scenarios  Contributor(s): Brian Winkel
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.

1108SPoissonProcess
27 Aug 2018  Modeling Scenarios  Contributor(s): Brian Winkel
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.

1108TPoissonProcess
27 Aug 2018  Modeling Scenarios  Contributor(s): Brian Winkel
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.

1032TDigoxinElimination
17 Aug 2018  Modeling Scenarios  Contributor(s): Brian Winkel
We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``firstorder reaction'' in the language of pharmacokinetics  the study of how drugs move in the body. This activity can be used to introduce compartmentalized...

6007SFunctionsAndDerivativesInSIRModels
12 Aug 2018  Modeling Scenarios  Contributor(s): Brian Winkel

6007TFunctionsAndDerivativesInSIRModels
12 Aug 2018  Modeling Scenarios  Contributor(s): Brian Winkel
Given a system of differential equations, how do the solution graphs compare with the graphs of the differential equations? Students tackle this question using SIR models for wellknown infectious diseases. The students view graphs both of solution curves and of the differential equations in the...

5026TEvictions
12 Aug 2018  Modeling Scenarios  Contributor(s): Brian Winkel
In this project, students develop two SIS models to study eviction trends in a population of nonhomeowner households using an actual eviction rate. (The Eviction Lab at Princeton University has developed a nationwide database of evictions based on 83 million eviction records.) As the first...

6070TBeerBubbles
24 Apr 2018  Modeling Scenarios  Contributor(s): Brian Winkel
The goal of this project is to set up and numerically solve a firstorder nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top. The system solution is then used to verify...

2017AllaliMathModelingOfAdaptiveImmunieResponsesHBVInfection
07 Mar 2018  Potential Scenario Ideas  Contributor(s): Brian Winkel
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...

2003RasmussenKeynesLinesOfEigenVectorsSolutionsToSytemsOfLinearDifferentialEquations
03 Mar 2018  Potential Scenario Ideas  Contributor(s): Brian Winkel
Rasmussen, Chris and Michael Keynes. 2003. Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations. PRIMUS. 13(4): 308320.Abstract: The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of...

2011Gaff EtAlOptimalControlManagementTickBorneDisease
03 Mar 2018  Potential Scenario Ideas  Contributor(s): Brian Winkel
Gaff, Holly D., Elsa Schaefer, and Suzanne Lenhart. 2011. Use of optimal control models to predict treatment time for managing tickborne disease. Journal of Biological Dynamics. 5(5): 517530Abstract: Tickborne diseases have been on the rise recently, and correspondingly, there is an...

2009Das EtAl BioeconomicHarvestingJBioDynamics
03 Mar 2018  Potential Scenario Ideas  Contributor(s): Brian Winkel
Das, Tapasi, R. N. Mukherjee, and K. S. Chaurhur. 2009. Bioeconomic harvesting of a prepredator fishery. Journal of Biological Dynamics. 3(5): 447462.Abstract: This paper deals with the problem of nonselective harvesting of a prey–predator system by using a reasonable catchrate...