Reproduction number
How many people, on average, each infected person goes on to infect; above 1 an outbreak grows, below 1 it dies out.
The basic reproduction number, R₀ ("R nought"), is the average number of new infections caused by one infected person in a population where nobody is immune. The effective reproduction number, often just called R, is the same figure for the population as it stands now, after some people have become immune or changed their behaviour.
The crucial threshold is 1. If each case leads to more than one new case, the numbers grow, often exponentially. If each leads to fewer than one, the outbreak shrinks and dies out. Measles, one of the most contagious diseases, has an R₀ of about 12 to 18; the 1918 pandemic influenza is often put at about 2.
R is not a fixed property of a germ. It depends on how long people stay infectious, how many contacts they have and how easily the germ passes at each contact, all of which can change. Isolating the sick, cancelling crowded events, closing schools and vaccinating all push R down, and because growth compounds, acting early while cases are few prevents far more infections than acting later.
Epidemiologists often model outbreaks with compartment models such as the SIR model, which divides people into Susceptible, Infectious and Recovered and tracks how they move between the groups. As the pool of susceptible people shrinks, R falls; once enough people are immune, it drops below 1 and the outbreak fades. For measles that herd immunity threshold is about 92 to 94 per cent.
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