Modeling an Outbreak
Learning Objectives
Students will be able to:
- Define R0 (basic reproduction number) and explain its significance
- Predict outbreak growth patterns based on R0 values
- Calculate simple transmission chains using exponents
- Explain why some diseases spread faster than others
The Power of 2
Challenge: One person gets sick and infects 2 others. Each of those 2 infects 2 more. How many people are infected after 10 rounds?
| Round | New Cases | Calculation |
|---|---|---|
| 0 | 1 | Start |
| 1 | 2 | 21 |
| 2 | 4 | 22 |
| 3 | 8 | 23 |
| 5 | 32 | 25 |
| 10 | 1,024 | 210 |
From just ONE person, over a thousand can be infected! This is exponential growth.
Introducing R0 (R-naught)
R0 = The average number of people infected by one sick person in a population where everyone can get sick.
What R0 Tells Us
R0 < 1 R0 = 1 R0 > 1
Outbreak shrinks
(each case makes <1 new case)
Stable
(each case makes exactly 1)
Outbreak grows
(each case makes >1 new case)
R0 of Real Diseases
| Disease | R0 | How Contagious? |
|---|---|---|
| Measles | 12-18 | Extremely contagious |
| Chickenpox | 10-12 | Very contagious |
| COVID-19 (Omicron) | 8-15 | Very contagious |
| COVID-19 (Original) | 2-3 | Moderate |
| Common cold | 2-3 | Moderate |
| Seasonal flu | 1.3-1.5 | Lower |
| Ebola | 1.5-2.5 | Moderate (but contact spread) |
The Math of Exponential Growth
Example Comparison:
Flu (R0 = 1.4), 5 generations:
1.45 = 5.4 cases
Measles (R0 = 15), 5 generations:
155 = 759,375 cases!
This is why measles spreads so much faster than flu!
Activity: Calculate the Spread
Calculate new cases after 5 generations for each disease:
| Disease | R0 | Calculation | After 5 Generations |
|---|---|---|---|
| Disease A | 1.5 | 1.55 | ~7.6 cases |
| Disease B | 2 | 25 | 32 cases |
| Disease C | 3 | 35 | 243 cases |
| Disease D | 5 | 55 | 3,125 cases |
Good News: We Can Change R!
R0 isn't fixed—interventions reduce the effective R:
Vaccination
Fewer susceptible people = fewer potential infections
Masks
Reduce particles released and inhaled
Ventilation
Lower concentration = lower transmission probability
Isolation
Sick people don't spread if they stay home
If we can get R below 1, outbreaks shrink instead of grow!
Key Takeaway
R0 tells us how fast a disease can spread. When R0 > 1, cases multiply exponentially. Small differences in R0 lead to huge differences in outbreak size. The good news: we can use interventions to reduce effective R below 1 and stop outbreaks.