Building on their understanding of graphs, students are introduced to random processes on networks. They walk through an illustrative example to see how a random process can be used to represent the spread of an infectious disease, such as the flu, on a social network of students. This demonstrates how scientists and engineers use mathematics to model and simulate random processes on complex networks. Topics covered include random processes and modeling disease spread, specifically the SIR (susceptible, infectious, resistant) model.

During the early days of the coronavirus pandemic, we all made sacrifices to slow the spread of the virus and to flatten the curve of infections.The curve itself appears in the susceptible-infected-recovered (SIR) model – a simple epidemiological model that explains some of the basic dynamics of infectious disease. Curve-flattening effects of mitigation measures such as social distancing, mask wearing, and hand washing can be seen in the dynamics of the SIR model as can the phenomenon of herd-immunity.In this activity, students are encouraged to derive the SIR model from scratch and to explore dynamical features of the model such as curve flattening and herd immunity.These resources were created by Dr. Robert Kipka of Lake Superior State University. They are intended for high school students and teachers. Calculus or familiarity with families of functions such as logarithms is not required. However, in spite of the relatively modest mathematical background called for, this activity may be challenging.It may help to complete the Three Weeks in March activity before beginning.