## 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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