MR G.W. ROWE, HEAD OF BIOLOGY
In simple terms the R0 is a disease’s basic reproductive ratio - the number of cases at time zero measured compared to the number of cases at a future date. If there were 100 cases of disease X last week and 500 this week this would give a ratio of 1:5 and the R0 would be given as 5. Therefore, an R0 of 1.0 means the epidemic is infecting the same number of people over time and is not accelerating. An R0 of above 1.0 will lead to an exponential increase in the numbers infected and an R0 below 1.0 will lead to a decline in the numbers infected by the disease.
There are many complex interacting factors which determine R0 for example, method of transmission (airborne droplet = generally lead to higher R0 values than sexual transmission), period of time where those infected are able to transmit the disease and success in isolating those infected from the general population. But, in a nutshell, the first paragraph describes what most people need to know to interpret R0 values in the media.
The two graphs below show how numbers of infections change with different R0 values and highlight the rather scary nature of exponential growth when the R0 rises above the threshold of 1.0.
Left - (BBC News)1
Right - Illustration of cases at 4 time intervals with an R0 of 1.5 (The Wall Street Journal)2
Why is it important?
Firstly, the overall (average) R0 value for the entire country is being used by the Government to determine the ‘virus response level’ and inform how draconian restrictions are to limit the spread of the virus. If the R0 increases above 1.0 restrictions are tightened to a lockdown situation whereas, if the R0 is comfortably below 1.0 this allows for more individual freedoms without significant risk of uncontrolled exponential growth. The R0 is also used regionally to track the progress of the epidemic across the different regions of the UK to inform local policy and the potential regional easing of lockdowns and/or school opening in certain areas.
Crucially, the R0 value is also of great use in establishing herd immunity where either natural infections and recovery or a vaccine is used to give protection from the virus. During a growing epidemic, the maximum unvaccinated proportion of the population during herd immunity can be estimated by dividing 1 by the R0 value. This means a’ slow epidemic’ with R0 of 2 requires only around 50% of the population to be immune for herd immunity to take effect whereas a ‘fast epidemic’ with R0 of 5 would require 80% of the population to be immune to significantly slow the spread.
How useful is R0 as the Government’s most important headline measurement?
In combination with other measurements such as number of case, location of cases, age adjusted excess mortality etc… R0 can be a very useful measure, as described above, which gives information to help implement a strategy of viral suppression and adjustment of restrictions vs. individual freedoms. However, when the R0 is used alone in isolation this is deeply flawed and likely to lead to erroneous assumptions being made about the epidemic.
On its own an increase in R0 does not tell you whether measures to contain the epidemic have been successful or not. This is due to the nature of National and Regional R0 values being average measures which include cases in the community where the transmission rate is likely to be relatively low and Health/Care settings where transmission rates are inherently higher due to the increased concentration of vulnerable patients with significant co-morbidities. To explain this a little maths needs to be used:
Scenario A (before)
- in the community there at 1000 cases with an R0 of 1.0 in that setting.
- at the same time there are 1000 cases in Health/Care settings with an R0 of 3.0
- this gives an overall average R0 of 2.0 in that region.
If we now imaging the Government coronavirus strategy is highly successful in reducing community transmission and only modestly successful in reducing transmission within Health and Care settings (which is, after all, more of a challenge).
Scenario B (after)
- In the community there are 100 cases with an R0 of 0.5
- In Health/Care settings there are 800 cases with an R0 of 2.5
- When the numbers are crunched the average R0 is 2.28
Despite a decrease in number of cases across both settings and a reduction in R0 indicating that the Government’s strategy in slowing transmission has been highly successful the R0 has increased! This scenario demonstrates how an increase in R0 could either mean the strategy is not working and virus transmission is increasing or, it could mean the strategy is working but transmission in the community is falling much faster than in more challenging settings.
When presented with a single simple measure for tracking a complex situation this should trigger alarm bells but, the Government’s scientific advisors will be well aware of the limitations of R0 however, most of the public and most journalists will not be yet. It always pays to think how a single figure can be put into context and what else we need to know before jumping to conclusions.
I will leave you with the words of the great Hans Rosling:
“Data allows you political judgements to be based on facts, to the extant that the numbers describe reality”.
Bibliography
1 BBC News [online] ‘Coronavirus: What is the R number and how is it calculated?’
https://www.bbc.co.uk/news/health-52473523
2 The Wall Street Journal [online]’How Many People Might One Person With Coronavirus Infect?’ https://www.wsj.com/articles/how-many-people-might-one-person-with-coronavirus-infect-11581676200
3 BBC News [online]’ Coronavirus infection 'R' rate in UK creeps up’ https://www.bbc.co.uk/news/health-52677194
Firstly, the overall (average) R0 value for the entire country is being used by the Government to determine the ‘virus response level’ and inform how draconian restrictions are to limit the spread of the virus. If the R0 increases above 1.0 restrictions are tightened to a lockdown situation whereas, if the R0 is comfortably below 1.0 this allows for more individual freedoms without significant risk of uncontrolled exponential growth. The R0 is also used regionally to track the progress of the epidemic across the different regions of the UK to inform local policy and the potential regional easing of lockdowns and/or school opening in certain areas.
(BBC News)3
How useful is R0 as the Government’s most important headline measurement?
In combination with other measurements such as number of case, location of cases, age adjusted excess mortality etc… R0 can be a very useful measure, as described above, which gives information to help implement a strategy of viral suppression and adjustment of restrictions vs. individual freedoms. However, when the R0 is used alone in isolation this is deeply flawed and likely to lead to erroneous assumptions being made about the epidemic.
On its own an increase in R0 does not tell you whether measures to contain the epidemic have been successful or not. This is due to the nature of National and Regional R0 values being average measures which include cases in the community where the transmission rate is likely to be relatively low and Health/Care settings where transmission rates are inherently higher due to the increased concentration of vulnerable patients with significant co-morbidities. To explain this a little maths needs to be used:
Scenario A (before)
- in the community there at 1000 cases with an R0 of 1.0 in that setting.
- at the same time there are 1000 cases in Health/Care settings with an R0 of 3.0
- this gives an overall average R0 of 2.0 in that region.
If we now imaging the Government coronavirus strategy is highly successful in reducing community transmission and only modestly successful in reducing transmission within Health and Care settings (which is, after all, more of a challenge).
Scenario B (after)
- In the community there are 100 cases with an R0 of 0.5
- In Health/Care settings there are 800 cases with an R0 of 2.5
- When the numbers are crunched the average R0 is 2.28
Despite a decrease in number of cases across both settings and a reduction in R0 indicating that the Government’s strategy in slowing transmission has been highly successful the R0 has increased! This scenario demonstrates how an increase in R0 could either mean the strategy is not working and virus transmission is increasing or, it could mean the strategy is working but transmission in the community is falling much faster than in more challenging settings.
When presented with a single simple measure for tracking a complex situation this should trigger alarm bells but, the Government’s scientific advisors will be well aware of the limitations of R0 however, most of the public and most journalists will not be yet. It always pays to think how a single figure can be put into context and what else we need to know before jumping to conclusions.
I will leave you with the words of the great Hans Rosling:
“Data allows you political judgements to be based on facts, to the extant that the numbers describe reality”.
Bibliography
1 BBC News [online] ‘Coronavirus: What is the R number and how is it calculated?’
https://www.bbc.co.uk/news/health-52473523
2 The Wall Street Journal [online]’How Many People Might One Person With Coronavirus Infect?’ https://www.wsj.com/articles/how-many-people-might-one-person-with-coronavirus-infect-11581676200
3 BBC News [online]’ Coronavirus infection 'R' rate in UK creeps up’ https://www.bbc.co.uk/news/health-52677194