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Materials for Teaching the SIR Epidemic Model

Author(s): Glenn Ledder1, Michelle Homp1

University of Nebraska-Lincoln

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This web page contains materials created by faculty of the University of Nebraska-Lincoln Department of Mathematics to teach basic fundamentals of mathematical epidemiology.

Licensed under CC Attribution-NonCommercial-ShareAlike 4.0 International according to these terms

Version 1.0 - published on 14 Jun 2020 doi:10.25334/4H67-PT17 - cite this


The original motivation for these materials was not the emergence of COVID-19, but rather the need for education about the value of vaccination. Epidemic modeling cannot address the unsupported claims of harm caused by vaccines, but it can very clearly show the tremendous benefit that vaccination has in combating disease. This message will be critically important once a vaccine is available for COVID-19. In a poll taken in May 2020, only half of Americans said they will take a COVID-19 vaccine, while 20% said they will not. This is not surprising, given the support the anti-vaccination movement has at the highest levels of the United States government, but it is, of course, alarming. With somewhere between 50% and 80% of a community receiving a COVID-19 vaccine, it is quite possible that there will be insufficient herd immunity to protect those people who cannot take a vaccine, leaving the public health threat of COVID-19 to continue indefinitely.

Given our motivation, the material we present has two primary objectives:

  • Help students understand the patterns of epidemic disease outbreaks and the challenges they present;
  • Help students explore the effect of public health policies, such as isolation of symptomatic patients and prior vaccination, on the course of the outbreak.

We approach these objectives through materials for study of the standard SIR disease model. This model is ideal for general education in epidemiology, but it is not suited to modeling COVID-19.

The materials include a simulation activity that allows students to directly experience an epidemic as participants and a spreadsheet activity for exploring the behavior of the standard SIR epidemic model. 

Simulation: Each student's status (healthy, infectious, sick, recovered) is indicated by a colored card if in a physical setting or an electronic designation if in a virtual setting.  The simulation progresses in turns, in which individuals are randomly paired.  If one individual in a pair is healthy and the other is infectious or sick (both of which are contagious states), a die is rolled to determine if transmission occurs.  The infectious and sick stages last exactly one turn, so these individuals advance to the next state each turn until they are recovered, whereupon they are immune for the duration of the experiment.  The simulation ends when nobody is infectious or sick.  Students keep track of the counts in each category and plot graphs.

Spreadsheet: The spreadsheet is pre-programmed for the SIR model with optional isolation of the sick and pre-vaccination.  Pre-designed experiments can be used to explore the behavior of the model and the effects of control measures.  Other experiments can be added by instructors or students.


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