
1009SICUSpread
02 Jun 2015   Contributor(s):: Brian Winkel
We offer students the opportunity to model the percentage of voluntary nonprofit hospitals in the United States with Intensive Care Units during the period of 19581974.

1017SDiseaseSpread
04 Jun 2015   Contributor(s):: Brian Winkel
We offer a physical situation, using a grid and M and M candies, to simulate the spread of disease. Students conduct the simulation and collect the data which is used to estimate parameters (in several ways) in a differential equation model for the spread of the disease. Students ...

1018SLogisticPopGrowth
04 Jun 2015   Contributor(s):: Brian Winkel
We offer artificial (toy) and historical data on limited growth population situations in the study of protozoa and lead students through several approaches to estimating parameters and determining the validity of the logistic model in these situations.

1019SRocksInTheHead
04 Jun 2015   Contributor(s):: Brian Winkel
We describe an experiment and offer data from a previously conducted experiment on the perception of the individual mass of a collection of rocks in comparison to a 100 g brass mass. We lead students to use the logistic differential equation as a reasonable model, estimate the parameters,...

1022SSpreadOfTechnology
27 Nov 2015   Contributor(s):: Brian Winkel
We examine plots on the spread of technologies and ask students to estimate and extract data from the plots and then model several of these spread of technologies phenomena with a logistic differential equation model.

1023SRumorSpread
04 Jun 2015   Contributor(s):: Brian Winkel
We use a newspaper report on the spread of a rumor based on shares of articles on the Internet over a 5 day period to demonstrate the value of modeling with the logistic differential equation. The data shows and the intrinsic growth rates confirm that the false rumor spread faster than true rumor.

1024SMalariaControl
06 May 2016   Contributor(s):: David Culver
This project offers students a chance to make policy recommendations based on the analysis of models using both linear (exponential decay) and nonlinear (logistic growth) differential equations. The scenario is based on the deployment of the United States Army's 62nd Engineer Battalion to...

1033SSouthernBarbeque
22 Jun 2016   Contributor(s):: Troy Henderson
We offer raw data collected from two thermometers used in the smoking process of Southern barbecue. One thermometer measures the temperature inside of the smoke chamber and the other measures the internal temperature of the meat. This data can be used to model and predict the amount...

1067SModelingWithSigmoidCurves
18 Aug 2018   Contributor(s):: Natali Hritonenko
The assignment considers two wellknown models of population growth, VerhulstPearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or Sshape. The assignment contains two opposite, but related tasks:...

1081STumorGrowth
09 Jun 2018   Contributor(s):: Randy Boucher, Ryan Edmund Miller
Students will transform, solve, and interpret a tumor growth scenario using nonlinear differential equation models. Two population growth models (Gompertz and logistic) are applied to model tumor growth. Students use technology to solve the Gompertz model and answer a series of questions...

1084SGoingViral
31 Aug 2019   Contributor(s):: Bill Skerbitz
Students employ randomization in order to create a simulation of the spread of a viral disease in a population (the classroom). Students then use qualitative analysis of the expected behavior of the virus to devise a logistic differential equation. Finally, students solve the...

1100SEngineeringDemographics
20 Aug 2021   Contributor(s):: Brody Dylan Johnson, Elodie Pozzi
The goal of this activity is to show students how population models can be used to examine social issues. The students will examine three different population models and will use numerical methods to apply each model to demographic data for the percentage of engineering degrees awarded to women...

1102SCancerGrowth
29 Jul 2018   Contributor(s):: Jue Wang
This scenario guides students in the use of differential equation models to predict cancer growth and optimize treatment outcomes. Several classical models for cancer growth are studied, including exponential, power law, Bertalanffy, logistic, and Gompertz. They examine the behaviors of the...

1102CSCancerGrowth
19 Jan 2022   Contributor(s):: Jennie D'Ambroise
This module guides students in the use of differential equation models to predict cancer growth and study treatment outcomes. Several classical models for cancer growth are presented including exponential, power law, Bertalanffy, logistic, and Gompertz. Students solve firstorder differential...

1104SInfectionRisk
26 Aug 2021   Contributor(s):: Qingxia Li
This project is designed to examine differences between the exponential and logistic growth models in biology and how to apply these models in solving epidemic questions. This project was designed for an introductory section in Calculus II or a course involving ordinary differential equations,...

1111SSpreadOfInformation
02 Sep 2019   Contributor(s):: Jeff Pettit
Students perform experiments to model spread of information within a population. Students collect data, determine essential components and parameters and build a mathematical model which can be compared to predicted data, measured data, and modeled data. Part 3 can require students to move from...

1127SFishHarvestingStudentVersion
06 May 2020   Contributor(s):: Will Mitchell
We offer students a harvesting model for operating a fishery over a 25 year horizon and ask them to write a report on optimal harvesting policy with their analyses for fishing industry experts (not necessarily mathematicians).

1143SPopulationModelVariationsMATLAB
17 Feb 2019   Contributor(s):: Bill Skerbitz
Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models while learning some basic MATLAB functions for working with differential equations. They will also work with other utilities...

1170SCensusModelingStudentVersion
22 Dec 2021   Contributor(s):: Jean Marie Linhart, Gary William Epp
Students who have studied models for population are likely to be familiar with the exponential and the logistic population models. The goal here is to explore the role of modeling assumptions in choosing which model to use. We will compare and contrast the United States census data and the...

1190SIntroClass
05 Mar 2022   Contributor(s):: Bill Skerbitz
Students are led step by step through the development of introductory ideas in mathematical modeling with differential equations. They will encounter the fundamental ideas underlying unlimited population growth (exponential models), limited population growth (logistic models), and a coupled...