What is R0? The basic reproduction number, explained

R0, the basic reproduction number (pronounced "R naught"), is the average number of people one infected person would go on to infect in a population where nobody is immune and nothing is being done to stop the spread. The effective reproduction number, written Re or Rt, is the same idea applied to the real world, after immunity, changes in behavior and control measures are taken into account. When the reproduction number is above 1, each case leads to more than one new case on average and an outbreak grows; when it is below 1, the outbreak shrinks and can die out.

What the number means in practice

The reproduction number counts generations of infection, not days. Starting from 100 cases, here is what different values mean over four generations:

These are averages, and real outbreaks are much less tidy, especially when there are only a few cases. The table also says nothing about how long a generation takes. That depends on the disease's incubation and infectious periods (see incubation period), so two diseases with the same R0 can spread at very different speeds.

Why R0 is not a fixed number

An article in CDC's journal Emerging Infectious Diseases, Complexity of the Basic Reproduction Number (R0) (January 2019), explains that R0 is not a biological constant for a germ. It is estimated with mathematical models and rests on three main ingredients:

Because contact patterns differ from place to place, the article says an R0 worked out in one setting may not apply in another. Results also depend on the model structure, the assumptions and the data used, so different studies of the same disease often report different values. Measles is the article's example: it found more than 20 published R0 values for measles, ranging from 5.4 to 18, a wider spread than the 12 to 18 range that is often quoted. Some older estimates, it adds, have since become outdated.

R0 vs Re and Rt

CDC's Center for Forecasting and Outbreak Analytics notes on its page Rt: Estimating the direction of disease transmission (5 June 2026) that a fully susceptible population rarely exists in the real world. Rt is estimated from case data rather than measured directly. CDC also cautions that an Rt below 1 means infections are decreasing, not that transmission is low.

Vaccination, isolation and other measures do not change R0; they lower the effective reproduction number. The 2019 CDC journal article notes that an epidemic can end once that number falls below 1. This is the job of contact tracing: finding exposed people quickly, and separating those who fall ill, cuts the number of new infections each case causes and helps push Re below 1. The difference between those two steps is covered in isolation vs quarantine.

Superspreading and the dispersion parameter k

An R of 2 does not mean every case infects two people. In many outbreaks most infected people pass the germ to no one, while a few pass it to many. Those few are often called superspreaders, and gatherings where many people are infected at once are called superspreading events.

A 2005 study in Nature (full text on PMC) measured this unevenness with a dispersion parameter, k: the smaller k is, the more transmission is concentrated in a few people. For the 2003 SARS outbreak in Singapore, the study estimated that 73% of cases were each expected to infect fewer than one person, while 6% were each expected to infect more than eight. The authors found no general "20/80 rule" (20% of cases causing 80% of spread), but strong variation in many diseases. They described pneumonic plague transmission as slightly less variable than smallpox and mpox.

The study drew two practical points from this:

• When variation is high, a single imported case is more likely to fizzle out, because most cases infect nobody. With an R0 of 3, the study calculated about a 6% chance that one introduction dies out if every case is alike, but about 76% with SARS-like variation.
• Control aimed at individuals, such as tracing and isolating cases and their contacts, works better than spreading the same effort evenly across a whole population.

Published R0 estimates for pneumonic plague

CDC says droplets from the lung form are the only way plague spreads between people, and WHO says human-to-human transmission of bubonic plague is rare (see pneumonic plague). Estimates of its reproduction number come from a handful of historical outbreaks and the 2017 epidemic in Madagascar, often with incomplete records, and the studies use different methods. Published estimates range from below 1 for some single outbreaks to about 3.5:

Two patterns run through these studies. In the 2004 study, most transmission was to people caring for the sick, and outbreaks were brought under control quickly by isolating patients and tracing and isolating their contacts. The 2006 study found that the effective reproduction number in Mukden fell below 1 once control measures began, and the 2018 study linked periods of control in Madagascar to contact tracing and the delivery of antibiotics. The 2019 study adds a caution: part of the rise in reported cases may have come from more cases being found through contact tracing and public awareness, one reason these numbers are uncertain.

What about the suspected case in Irkutsk?

No health authority has published a reproduction number for the suspected plague case in Irkutsk, and PlaguePrimer does not estimate one. WHO's Director-General said on 7 October, relaying Russia's reply, that there were about 200 contacts. A contact is someone who may have been exposed, not a confirmed infection. For what is known so far, see what happened in Irkutsk and the latest updates.

What R0 does not tell you