Questions: Basic Reproduction Number and Epidemic Control

Question 1

If a pathogen has R₀ = 4, what proportion of the population must be immune (through vaccination or prior infection) to achieve herd immunity?

• A. 25%
• B. 50%
• C. 75%
• D. 100%

Answer: (C)

The herd immunity threshold is 1 − 1/R₀ = 1 − 1/4 = 0.75, or 75%. With R₀ = 4, each infected person would infect 4 others in a fully susceptible population; once 75% are immune, the average number of new infections per case drops below 1 and spread cannot be sustained.

Question 2

When the effective reproduction number (Rₜ) drops below 1 during an active outbreak, new cases stop occurring immediately.

• T. True
• F. False

Answer: False

Rₜ < 1 means each infectious person generates fewer than one new infection on average, so case counts will decline — but people already infected continue transmitting until they recover. The outbreak winds down exponentially rather than halting at once. Rₜ is a real-time signal of trajectory, not a switch.

Question 3

Why is R₀ not a fixed biological constant for a given pathogen, even though it is sometimes presented as one?

Model answer: R₀ is a product of three factors — the probability of transmission per contact, the average contact rate, and the duration of infectiousness — all of which vary with population density, social behavior, healthcare infrastructure, and any interventions in place. The same pathogen can have a very different R₀ in a dense urban setting versus a rural one, or before versus after behavior change campaigns.

Treating R₀ as a biological constant is the most common misunderstanding of the metric. Because contact rate and behavior are embedded in the estimate, published R₀ values are specific to the population and context in which they were measured, not universal properties of the pathogen itself.