SUCCEED

5 Minutes

Introduction to the SIR Model (5 min)

• Your School – one person is sick, how long will it take for the disease to spread through the whole school?
• What do we need to know in order to find that out? (write on the board)
  • How many people are there?
  • TOTAL = (Students provide)
    • How many people are sick at first?
  • INITIAL INFECTED = (Students provide)
    • Susceptible = Total – Infected

10 Minutes

One-day scenario (10 min)

• Create 4 columns
  • Day
  • Susceptible
  • Infected
• In Column F, enter constants (Name them!)
  • Total
  • Initial Infected
• Enter values for Total and Initial Infected
  • Day = 1
  • Infected = Initial Infected
  • Susceptible = Total – Infected
• What happens if we change the Initial Infected?
• What happens if we change the Total?
• Add scroll bars to Total and Initial Infected.

The standard 50-minute lesson does not include physical modeling. If there is extra time, students can play the SIR game during this time (see attached material)

Build the full model (30 min)

• Open a new sheet in Excel
• How do we find out how many people will get sick each day?
  • Interactions between susceptible and infected
  • Possible Interactions = S * I
  • Actual Interactions = Possible * Interaction Rate
  • Infectious Interactions = Actual * Infection Rate
  • ∆Infected = S * I * Interaction rate * Infection Rate
• Interaction rate = % people you interact with
• Infection rate = % interactions result in infection
• Equations are the same as before!
  • Infected = Infected + ∆Infected * ∆Time
  • Susceptible = Susceptible - ∆Infected * ∆Time
• Columns:
  • Day
  • Susceptible
  • Infected
  • Recovered
• Constants (name these!):
  • Total
  • Initial Infected (slider bar)
  • Delta Time (slider bar)
  • Interaction Rate (slider bar)
  • Infection Rate (slider bar)
• Enter Time
• Use formulas in Susceptible and Infected Columns
• Add slider bars
  • Demonstrate how they need to be converted to get a fraction
• Build a graph

Allow students to explore their models and make observations about the shape of the graph lines. Here are some example questions:

• Why do the graph lines level off at the end?
  • (constant population, disease can’t spread beyond the limit)
• What could be added to this model to make it more realistic?
  • (vaccination, recovered become susceptible again, randomness)
• How could scientists use this model?
  • (Study the affects of different diseases on a population, according to contagiousness)

With extra time, you can also build a recovered column:

• Adding Recovered
  • ∆Recovered = I Before * Recovery Rate
  • Infected = I Before + (∆Infected – ∆Recovered) * ∆Time
  • Recovered = R Before + ∆Recovered * ∆Time