- 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
The attached supporting materials include:
- Project Instructions
- Intermediate Deliverables
Project Description (Acrobat (PDF) 322kB Oct10 20)
Project Rubric (Acrobat (PDF) 130kB Oct10 20)
The SIR Model (Acrobat (PDF) 195kB Oct10 20)
Compartment Modelling (Acrobat (PDF) 183kB Oct10 20)
Teaching Notes and Tips
- SIR model
- 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.
References and Resources