4
Explain
The Math of Epidemics
Duration
45 minutes
Type
Explain / Elaborate
Standards
MS-LS2-1, 8.F.B.5
Learning Objectives
Students will be able to:
- Calculate doubling time for disease outbreaks
- Interpret epidemic curves (epi curves)
- Identify growth, peak, and decline phases
- Explain why "flattening the curve" matters
Doubling Time
Doubling time = How long it takes for the number of cases to double. Shorter doubling time = faster spread!
Finding Doubling Time
Outbreak A:
| Day | Cases | Pattern |
|---|---|---|
| 1 | 10 | Cases double every 2 days |
| 3 | 20 | |
| 5 | 40 | |
| 7 | 80 | |
| 9 | 160 |
Doubling time = 2 days
Outbreak B:
| Day | Cases | Pattern |
|---|---|---|
| 1 | 5 | Cases double every 3 days |
| 4 | 10 | |
| 7 | 20 | |
| 10 | 40 |
Doubling time = 3 days (slower spread)
Reading an Epidemic Curve
An epidemic curve (epi curve) shows new cases over time:
Cases
| PEAK
| / \
| / \
| / GROWTH \ DECLINE
| / \
| / \
|/_____________________\____
Start Time
| Phase | Graph Shape | R Value | What's Happening |
|---|---|---|---|
| Growth | Steep upward | R > 1 | Cases multiplying rapidly |
| Peak | Top of curve | R ≈ 1 | Maximum daily cases |
| Decline | Downward slope | R < 1 | Cases decreasing |
| End | Low and flat | R << 1 | Outbreak ending |
"Flatten the Curve"
Without Intervention
- High, sharp peak
- Healthcare overwhelmed
- More deaths
- Faster but worse
With Intervention
- Lower, wider curve
- Healthcare can cope
- Fewer deaths
- Slower but better
Key insight: Both curves can have the same TOTAL cases, but spreading them out saves lives!
Activity: Analyze an Outbreak
Spring Flu Outbreak at Lincoln Middle School
| Week | New Cases | Total Cases |
|---|---|---|
| 1 | 3 | 3 |
| 2 | 8 | 11 |
| 3 | 22 | 33 |
| 4 | 48 | 81 |
| 5 | 85 | 166 |
| 6 | 120 | 286 |
| 7 | 95 | 381 |
| 8 | 62 | 443 |
| 9 | 31 | 474 |
| 10 | 12 | 486 |
Questions:
- What week was the peak?
- During weeks 1-5, was R greater or less than 1?
- During weeks 7-10, was R greater or less than 1?
- What's the approximate doubling time during growth phase?
Key Takeaway
Epidemic curves help us visualize and understand outbreaks. During growth phase, R > 1 and cases multiply. At the peak, R ≈ 1. During decline, R < 1. Interventions can "flatten the curve"—lowering the peak and spreading cases over time so healthcare systems aren't overwhelmed.