Interactive parameter fitting + scenario analysis + prediction challenge
A school of 1,500 students is hit by a flu outbreak. The nurse recorded daily counts for 28 days — but you can only see the first 14 days.
The population is divided into three compartments:
The SIR model equations:
Basic reproduction number:
Your tasks:
| Day | S | I | R |
|---|---|---|---|
R₀
RMSE
Q1. If R₀ = 4.5 for this outbreak, what does it mean?
Q2. If R₀ = 4.5, what minimum fraction of students must be vaccinated to prevent an outbreak?
Q3. The school mandates masks, reducing β by 50%. What happens?
Q4. A new medicine halves the infectious period (γ doubles). Which is most accurate?
Q5. If the outbreak started with 50 infected instead of 5, what changes the MOST?
Q6. In the SIR model, the infected count I(t) starts to DECREASE when:
Train RMSE
Test RMSE
Peak Day
You: / Actual:
Peak I
You: / Actual:
β
0.00030
γ
0.100
I₀
5
R₀
4.50
Herd immunity: 1 − 1/R₀ = 1 − 1/4.5 ≈ 78%
Peak condition: I peaks when S = γ/β = 0.1/0.0003 ≈ 333
Key insight: I₀ shifts the epidemic timeline but barely changes total infections or peak height. R₀ = βN/γ controls everything — it determines IF the epidemic spreads, HOW MANY get infected, and HOW HIGH the peak reaches.