📋 Activity Overview

Students build a simple SIR model in a spreadsheet for a fictional city of 1 lakh people, varying transmission rate, recovery rate, and vaccination — discovering how small parameter changes lead to dramatically different outcomes.

💡 Teacher Tip

The most powerful experiment is adding vaccination (starting with some R population). Students often expect linear benefit: 10% vaccinated = 10% fewer cases. The actual result — a dramatically lower peak — demonstrates herd immunity and exponential dynamics in one concrete moment.

🎯 Learning Objectives

  • ✓ Understand the SIR model as a mathematical abstraction of disease spread
  • ✓ Build iterative calculations in a spreadsheet (computational thinking in practice)
  • ✓ Observe how small changes in β and γ parameters produce dramatically different outcomes
  • ✓ Connect simulation results to real COVID-19 policy decisions

🗂️ Materials Needed

Computer or tablet with spreadsheet software SIR model template (pre-built with parameter cells) Parameter variation worksheet Graph paper for sketching Printed model equations Discussion handout on COVID policy

📌 Step-by-Step Instructions

Introduce the Model (8 min) — Explain S (Susceptible), I (Infectious), R (Recovered/Removed). Show the equations: dS/dt = -βSI/N; dI/dt = βSI/N - γI; dR/dt = γI. Connect to R0 = β/γ.
Set Up the Spreadsheet (10 min) — Open template. City population: 1,00,000. Day 0: S=99,999, I=1, R=0. β=0.3, γ=0.1. Each row = one day. Fill in formulas for Day 1.
Extend the Model (8 min) — Drag formulas to Day 180. Generate a chart: S, I, R over time. What does the peak of I mean? When does I start falling?
Parameter Experiments (15 min) — Experiment 1: Change β to 0.5. What happens to peak infection? Experiment 2: Change γ to 0.2. How does faster recovery change the curve? Experiment 3: Start with 10% already recovered (vaccinated). How does this shift the peak?
Policy Simulation (8 min) — 'On Day 30, the government introduces a lockdown that halves β. Implement this: from Day 30 onwards, β=0.15.' How does the curve change? What if lockdown starts on Day 60?
Interpret and Present (6 min) — Each pair writes: 'The most impactful change we found was ___ because ___.' Present to class.
Limitations Discussion (5 min) — What does the SIR model miss? (Age groups, healthcare capacity, geographic spread, variants, vaccine waning immunity.) 'This is abstraction — the simplification teaches us the core logic, but real models are far more complex.'

🧠 CT Pillar Connections

Algorithmic Thinking
The SIR spreadsheet is an iterative algorithm: repeat a calculation (new S, I, R) 180 times with the previous day's output as input. This is the computational core of all simulation models.
Abstraction
The entire complexity of a pandemic — human behaviour, healthcare systems, viral biology — is abstracted to 3 variables and 2 parameters. Powerful but incomplete.
Pattern Recognition
Students discover the universal 'epidemic curve' pattern — a rapid rise, peak, and decay — and see how parameters shift this pattern without changing its fundamental shape.

💬 Discussion Questions

  • Why does a 10% reduction in transmission (β) reduce the peak by much more than 10%?
  • At what percentage of recovered/vaccinated people does the epidemic fail to take off at all? (Herd immunity threshold)
  • What decisions did the Indian government make during COVID that you could model with this simulation?
  • If you were advising ICMR, what would you include in your model that the SIR model misses?