SUCCEED

5 Minutes

Introduction to the SIR Model (5 min)

• At your School - if 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 at the school? (Total Number of People)
    • TOTAL = (Students provide)
      • A good number might be around 1000.
  • How many people are sick at first? (Infected)
    • INITIAL INFECTED = (Students provide)
      • A good number would probably be 1.
  • How many aren't sick right now, but could get sick? (Susceptible)
    • SUSCEPTIBLE = TOTAL - INFECTED
      • In other words, out of the total population of the school, whoever isn't sick must be well and susceptible to getting sick.

10 Minutes

Start building your model!

• Create 3 columns
  • A = "Time"
  • B = "Susceptible"
  • C = "Infected"
• In Column G enter the names of the constants. In column H, write the constants themselves.(Don't forget to name them!)
  • Total
  • Initial Infected
• Enter values for Total and Initial Infected
  • A2 = 0 (Initial Value of Time)
  • B2 = TOTAL - INFECTED
  • C2 = INITIAL INFECTED
• What happens if we change the Initial Infected?
  • More people are initially sick.
• What happens if we change the Total?
  • More people in the school who could possibly get sick.
• 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)

• How do we find out how many people will get sick each day?
• To figure this out, we are first going to have to figure out how many possible interactions between infected and susceptible people there are (we don't care about interactions between infected people and other infected people or susceptible people and other susceptible people, because those won't change the number of infected or susceptible people). How do we find out how many possible interactions there are? Use this example to help students: Hold up two fingers on one hand and three on another. If you want to touch each finger on one hand (infected) to each finger on the other hand (well) once, how many times would you touch your fingers together? Answer: 3*2 = 6 times. In our model, it works the same way.
• How do we calculate the number of possible interactions between infected and susceptible people?
  • Interactions between susceptible and infected
  • Possible Interactions = S * I
  • Actual Interactions = Possible * Interaction Rate
  • Infectious Interactions = Actual * Infection Rate
  • delta 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 + delta Infected * delta Time
  • Susceptible = Susceptible - delta Infected * delta 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
  • delta Recovered = I Before * Recovery Rate
  • Infected = I Before + (delta Infected - delta Recovered) * delta Time
  • Recovered = R Before + delta Recovered * delta Time