The Basic Reproduction Number R0
Learning Objectives
- Define R0 and explain its epidemiological significance
- Calculate R0 from transmission and recovery parameters
- Apply the epidemic threshold theorem (R0 > 1 for outbreak)
- Calculate herd immunity threshold from R0
- Distinguish between R0 and effective reproduction number Rt
The Big Question
"What single number tells us whether an epidemic will spread or die out?"
Defining R0
R0 = average number of secondary infections caused by one infected individual in a fully susceptible population
R0 = beta / gamma
R0 for Common Diseases
| Disease | R0 | Herd Immunity Threshold |
|---|---|---|
| Measles | 12-18 | 92-95% |
| Pertussis | 12-17 | 92-94% |
| COVID-19 (original) | 2.5-3.5 | 60-70% |
| COVID-19 (Omicron) | 8-15 | 87-93% |
| Seasonal flu | 1.3 | 23% |
The Epidemic Threshold
R0 > 1: Epidemic
Each case generates more than one new case. Disease spreads exponentially initially.
R0 < 1: Die Out
Each case generates less than one new case. Disease cannot sustain spread.
Herd Immunity Threshold
HIT = 1 - 1/R0
The fraction of the population that needs to be immune to prevent epidemic spread.
Activity: R0 Calculations
- A disease has beta = 0.5/day and infectious period of 5 days. Calculate R0. Will an outbreak occur?
- If interventions reduce transmission by 50%, what is the new Reffective?
- For R0 = 4, what fraction of the population needs immunity to achieve herd immunity?
- How does improving ventilation (which reduces beta for airborne diseases) affect R0?
Key Takeaway
R0 is the fundamental quantity determining whether an epidemic can spread. Any intervention that reduces R below 1 will eventually stop the outbreak. For airborne diseases, improving indoor air quality directly reduces the transmission rate beta, lowering R0 and making outbreaks less likely or less severe.