# Unprecedented

## Summary

This project is designed to introduce lower-division science and engineering students to mathematical modelling through the analysis of real-world data related to the novel coronavirus global pandemic. The project guides students along an exploration of data collection, physical models, Euler Method, partial differential equations, and Monte Carlo simulations.

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## Learning Goals

Students will:
- discuss the meaning of partial differential equations and applied coefficients when implementing epidemiological models of the susceptible, infected, recovered populations.
- apply Euler's method, explicit solutions and Monte Carlo simulations in the discussion of their model and the associated uncertainty of their data set
- create linear and logarithmically scaled plots of data and modelled populations to visualize the effects of population density, demography, and government policy changes.

MATLAB is mainly used as a problem-solving and graphing/visualization tool for this project. It allows students to learn that MATLAB can be used in the development of numerical models, and allows them to relate the concepts they learn in the context of real-world science and problem-solving. The technical skills that students are expected to have going into this project are mostly related to concepts learned in calculus; such as the evaluation of integrals, initial conditions, boundary conditions, linearization, error propagation, linear algebra and ordinary differential equations.

## Context for Use

The project was designed to be completed in an introductory, lower-division programming course for science and engineering students. The project can be completed individually or as a class activity; and should take 2-3 weeks to complete.

To complete the project, students need to be able to import data from an Excel file, employ differential equations and Euler's Method, plot linear and non-linear trends, and use fminsearch. As this project is designed to introduce students to epidemiological modelling approaches, no prior knowledge of infectious diseases is needed. While this project was developed for use in a course based on engineering problem-solving, particularly using MATLAB as a tool; it can also easily be used as a classroom activity for mathematical and scientific modelling in an introductory programming course.

## Description and Teaching Materials

As an open-ended course project, it will be helpful for the instructor to clarify the final deliverable, and provide class time for scaffolding. In particular, the instructor needs to determine which locations each student will consider and the format of the final submission (technical paper, presentation, etc.). In my execution of the project, I have used half of the class time during those two weeks (6 hours) to motivate the project, discuss the constraints of our engineering approach, facilitate a class computational activity using the SIR model, and discuss relevant plotting options in MATLAB. The other half of the class time was used for peer reviews, small group activities and student led discussions related to the intermediate deliverables. The intermediate deliverables (supporting activities and assignments) are graded separately, as other class laboratory activities are, during the two weeks prior to the final deliverable submission. The intermediate deliverables do not directly impact the final deliverable's scoring. The intermediate deliverables also serve guide students in the development of their numerical models and their time management. I select three different locations for each student and have them submit a individual technical report as their final submission.
The attached supporting materials include:
- Project Instructions
- Rubric
- Intermediate Deliverables
Project Description (Acrobat (PDF) 322kB Oct10 20)
Project Rubric (Acrobat (PDF) 130kB Oct10 20)
The SIR Model (Acrobat (PDF) 329kB Dec17 20)
Compartment Modelling (Acrobat (PDF) 183kB Oct10 20)

## Teaching Notes and Tips

It is useful to conduct classroom activities on the following topics after introducing the larger project:
- SIR model
- fminsearch
- Monter Carlo simulations
- Compartment modelling
- Ordinary Differential Equation Solvers

Scaffolding the project with in-class activities will provide opportunities to work through each component in MATLAB. I will discuss ideas for scaffolding in the assessment section below.

## Assessment

The first intermediate deliverable should be use to allow students to collect data on their assigned locations and create an initial 2D linear and non-linear plots. The second intermediate deliverable should allow for an initial development of epidemiological models of the data they collected and identification of which parameters are constant, and which are time-dependent. The third intermediate deliverable should use information from testing and government policies to validate model parameters. The intermediate deliverables provide formative assessments on the content needed for the final deliverable.

## References and Resources

Additional resources that may be provided for students are listed below: