Epidemiology · Reference
What is the basic reproduction number?
The basic reproduction number, R0, is the average number of new infections caused by one infectious individual in a population that is entirely susceptible. It is a fundamental measure of how transmissible an infectious agent is, and it shapes thresholds for population immunity.
What R0 represents
R0 (pronounced "R-nought") is defined for the specific situation of a fully susceptible population with no immunity and no control measures. It captures the average number of further cases one infectious person would generate in that idealised setting. Its value depends on three broad factors: the probability of transmission per contact, the rate of contact between people, and the duration over which an individual is infectious. Because it bundles these together, R0 is a property of the agent and the population and setting, not of the agent alone, and the same pathogen can have different R0 values in different contexts.
The threshold at R0 = 1
The critical value is 1. When R0 > 1, each case more than replaces itself on average, so the number of infections can grow and an outbreak can take off. When R0 < 1, cases fail to replace themselves and transmission tends to fade. This threshold also underlies the herd immunity concept: the proportion of a population that needs to be immune to halt sustained spread is approximately 1 − 1/R0, so a higher R0 implies a higher immunity threshold.
R0 versus the effective reproduction number (Rt)
R0 assumes everyone is susceptible, which is rarely true once an infection is circulating. The effective reproduction number, written Rt or Re, is the average number of secondary cases per infectious person at a given time, given the immunity and control measures actually present.
As immunity builds or measures take effect, Rt falls below R0. The goal of many control efforts is to push Rt below 1, at which point an epidemic shrinks. R0 describes baseline transmissibility; Rt describes the situation as it actually unfolds.
Use and cautions
R0 is widely used to compare the transmissibility of infections and to inform models of how outbreaks might progress. It must be interpreted with care: published values are estimates that depend on assumptions, methods and the population studied, so a single headline figure can be misleading. R0 also says nothing about the severity of an infection — only about its spread. This page defines R0 generically as an epidemiological concept and does not provide guidance on any specific disease or situation.
Key facts
At a glance
- Definition: Average new cases from one case in a fully susceptible population
- Symbol: R0 ("R-nought")
- R0 > 1 / < 1: Can spread / tends to die out
- Depends on: Transmission per contact, contact rate, infectious period
- R0 vs Rt: Rt accounts for immunity and control already present
Common questions
FAQ
What does R0 mean?+
R0, the basic reproduction number, is the average number of new infections that one infectious person would cause in a population where everyone is susceptible and no control measures are in place. It is a baseline measure of how transmissible an infectious agent is.
What is the difference between R0 and the effective reproduction number?+
R0 assumes a fully susceptible population, while the effective reproduction number (Rt or Re) is the average number of secondary cases at a given time, accounting for the immunity and control measures actually present. Rt typically falls below R0 as immunity builds or measures take effect.
Does a high R0 mean a disease is more dangerous?+
Not necessarily. R0 measures how readily an infection spreads, not how severe it is. A disease can have a high R0 but cause mild illness, or a lower R0 but be more serious. Severity is captured by separate measures such as the case fatality rate.
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