In epidemiology, the basic reproduction number of an infection is the number of people a single infected individual will infect, in a population with no immunity to the disease. It is denoted R₀ (this is used as shorthand both in mathematical formulae and in prose).

When

R₀ < 1

the infection will die out. But if

R₀ > 1

the disease will spread exponentially, so there will be a large epidemic. This, however, cannot continue indefinitely: eventually the number of susceptible individuals will be depleted. They will either have died, or have survived infection and gained immunity to the disease, so limiting the spread of infection.

If

R₀ = 1,

then the infection will become endemic in the population.

The larger the value of R₀, the harder it is to control the epidemic.

Values of R₀ of some well-known infectious diseases:

• SARS: 0.84¹
• AIDS: 2-5
• Measles: 16-18

1. There is some controversy as to this value. As 0.84 has been calculated from data from the 2003 outbreak, which was tightly controlled by quarantine measures rather than being allowed to run its course, it has been argued that this value is invalid for the disease itself (as opposed to that particular outbreak) and 2-3 would be closer to the mark. Go through the calculations yourself (requires Powerpoint).