Understanding Predictions: What is R-Naught?

By Anders Gunderson and Liana Woskie, HGHI

In an outbreak, the question of how quickly a new pathogen spreads from one case to many is an essential piece of the puzzle scientists try to put together. To answer this question, experts use models that provide estimates, drawing from different sources of information. The outcome of this complex modeling process is a basic reproduction number, or R0, that tells us, on average, how many people an infected person can infect.

What is R-naught?
R-naught (R0) is a value that can be calculated for communicable diseases. It represents, on average, the number of people that a single infected person can be expected to transmit that disease to. In other words, it is a calculation of the average “spreadability” of an infectious disease.

Why is it Useful?
R0 provides valuable insight into the potential spread of a disease that local, state, and national governments, as well as public health authorities can use to factor into their decision making to best control the . Also, since it can be calculated for various diseases, it allows us to contextualize an outbreak with ones we have seen previously, such as SARS, MERS, Ebola, AIDS, seasonal flu, 2009 H1N1 flu pandemic etc.

How is it Calculated?
There are three main factors used to calculate R0. They are the infectious period of the disease, the mode of transmission, and the contact rate. We’ll dive a little deeper into each.

Infectious Period
This is the duration that a person infected is able to transmit that infection to another human — how long a person with the disease is contagious. Longer infectious periods mean higher R0 values.

Mode of Transmission
This is how the disease is spread. Airborne infections, like the flu, will spread more quickly than those requiring physical contact to be transmitted, like HIV or Ebola. Therefore, airborne infections tend to have higher R0 values.

Contact Rate
This refers to how many people a person with the disease can be expected to come into contact with. This variable is not specific to a disease like the first two. Rather it is impacted by numerous factors, including location and public health measures in place, such as quarantines or travel bans. This factor is considerably modifiable.

Sources of Uncertainty in R0 in the 2019-nCoV Outbreak 

Infectious Period
This variable is relatively fixed for a given infection — but it can vary somewhat from person to person. For example, a younger, otherwise healthy person may be infectious for less time than an older person with underlying health conditions. In the case of 2019-nCoV, we have estimates for the infectious period based on initial cases, but these values remain estimates. This also raises the point that R0 is an average, and the values from which it is calculated, including the infectious period, are also averages, meaning there can be considerable variability.  For example, when there are superspreaders with a high R0, this will be offset by most of the population actually having low R0.

Mode of Transmission
This variable is also relatively fixed for a given infection, but similarly to the infectious period, we aren’t sure exactly how 2019-nCoV is spread. Several early studies suggest that large airborne droplets, like what might be produced from the cough of an infected person, can transmit the disease, but there has been confusion about whether people with 2019-nCoV are infectious before developing symptoms. For example, an article published in The New England Journal of Medicine on January 30th that documented evidence for asymptomatic transmission of 2019-nCoV has now been reported to be based on faulty information. We are still learning about this virus, and any R0 values produced thus far can only be calculated based on the information at hand.

Contact Rate
This is where things start to get a little more complicated. The contact rate of an infected patient can vary wildly from person to person and depends on numerous variables including geography, travel patterns, quarantines or travel bans, and the ability of a healthcare system to effectively identify and isolate infected patients to name a few. This value, unlike the infectious period or mode of transmission, is highly modifiable. Higher contact rates mean higher R0 values, but all of these factors have to be estimated based on the context of the outbreak. In the case of 2019-nCoV, a recent paper in The Lancet estimated daily travel volumes and accounted for public health interventions, such as quarantines, to produce their estimates. 

R0 of 2019-nCoV in Context

R0 is often graphed alongside a disease’s mortality rate, such as in this NYT interactive (scroll down) or this visualization. This is a helpful way to get an idea both of a disease’s “spreadability” and how lethal it is, compared to others, but it is not without problems. At this stage, the mortality rate of 2019-nCoV cannot be accurately calculated because we don’t know the true number of total cases – it is therefore an estimate based on what we know as of now, much like R0. So, such graphs provide some context for where 2019-nCoV stands compared to other infectious diseases, but we should note that simply seeing that 2019-nCoV doesn’t appear to be all that fatal or spreadable, does not mean that the reality of the outbreak will play out that way.

What Does This All Mean?
This highlights the inherent complexity and variability of outbreaks.  R0 values can be helpful in gauging outbreak severity, but a high R0 value does not guarantee a world-wide spread, or a pandemic. It is a calculation of an average value that is based on estimates of averages. When early R0 values are produced, they should be circulated with care and guidance on how to interpret them. We have seen public alarm around R0 estimates with this current outbreak, which is exactly what we should aim to avoid.