Reproduction number - what is it and why is it important?

Reproduction number tells us how rapidly a virus spreads or declines.

The reproduction number, (sometimes Rn or R0 for short) is a key value describing how rapidly a virus spreads or declines. It is the average number of new people that a carrier will infect. If this number is exactly one, then every carrier gives the disease to one other person before they recover. That person goes on to give it to one other person before they recover, then they give it to one other person before they recover and so on. This would mean that the disease was stable and neither spreading, nor dying out. If Rn is bigger than one, then more people are catching the disease than are recovering. The disease will spread exponentially if it is left unchecked, like branches on a tree one splitting into two and splitting again. Conversely if Rn is less than one, more people are recovering from the disease than are catching it and the disease is declining.

What determines reproduction number?

Reproduction number is determined by a number of things, both how well the virus spreads and human factors, such as how closely people interact. Some things that can affect the reproduction number are:

• Virulence of the disease
• How long the disease can survive outside the body
• How the disease spreads (sneezing, touch, sexual transmission)
• Death rate
• Duration of infection
• Hygiene (washing hands, covering mouth when sneezing and coughing)
• Safe sex techniques
• Immunity (natural and vaccination)
• Travel
• Population density
• Sanitation

As you can see, some of these things are specific to the disease itself. Different diseases spread for different reasons. Ebola is incredibly virulent and a person with Ebola releases huge numbers of virus in their sweat and other bodily fluids. However, a person with Ebola is very obviously ill and often will not survive very long to pass it to many people. By contrast HIV requires sexual contact, so is much harder to transmit, however the person can be carrying the virus for years before showing any outward symptoms. This has meant that HIV became a worldwide pandemic, while Ebola did not.

Importantly people can reduce Rn by taking action such as getting immunisations, washing their hands, avoiding people who are ill. In extreme cases, such as with Coronavirus, self isolation can significantly reduce Rn.

Reproduction number for Coronavirus

It is still early in the Coronavirus outbreak and hence the value for Rn is not clear. Also because Rn depends on human factors, not just the virus, it may vary from place to place. This study estimated Rn for Coronavirus in Wuhan to be around 2.35. Another study found a value of 2.28 This means that every person who catches it spreads it to approximately two or three other people. Because this is significantly larger than 1, the virus has been able to spread around the globe. In order to eradicate the virus, we must use human factors to reduce Rn to below 1. Once this occurs the virus will begin to die out.