SIR Model -- Notes for the Instructor

Purposes:

• To develop the SIR Model for the spread of an infectious disease, including the concepts of contact number and herd immunity;
• to develop a version of Euler's Method for solving a system of differential equations

Prerequisites:

• The concept of derivative and the Chain Rule;
• The concept of autonomous first-order differential equation;
• At least surface understanding of Euler's method as a tool for generating an approximate numerical or graphical solution of a first-order equation;
• Some experience with the selected CAS.

This module was developed for use in a first-semester differential calculus course to stimulate interest in the derivative as a tool for modeling rate of change, as well as belief that useful information can be gleaned from hypotheses about rates of change. This is typically not the student's first exposure to Euler's method. The new concepts here are first-order systems of differential equations and application of the same Euler idea to a system.

While the language is kept as simple as possible for calculus students, the module could also be used early in a differential equations course for students who have not seen these concepts in their calculus course.

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