How Do I Measure: the Spread of a Virus?
COVID-19, the infectious disease caused by the newly discovered novel coronavirus, is (as I write this) a growing global pandemic. It's also measurable in several different ways including R0, a measure of how many people will be newly infected by a contagious person, essentially measuring the spread of the virus.
It's All In The Variables
I'm writing this on April 2, 2020 and given how fast the novel coronavirus (the virus that causes COVID-19) is spreading, what is true today will definitely not be true tomorrow. There are plenty of reliable sources to find out how to react to the virus in your area (in the US, I recommend the CDC which has easily accessible information for non-scientists). So I won't attempt here what those more knowledgeable people are doing, but I will add something for people who like learning how things are measured.
| Everything is measurable. Even a virus.
COVID-19 is being regularly compared to SARS (Severe Acute Respiratory Syndrome), H1H1 (commonly called the swine flu), as well as the seasonal flu for which many people get vaccinated every year. In those comparisons, I've seen arguments on social media about which of these is "worse" based on how quickly they spread, the mortality rate, or the presence (or absence) of medications. <sarcasm>Heaven knows I don't object to getting my medical news from memes </sarcasm>, but I wanted to know more about how a pandemic is measured and that led me to read about R0* (pronounced "R naught").
| Describing disease outbreaks
Sporadic - infrequent or irregular
Endemic - constant in a geographic area
Epidemic - sudden, unexpected increase in a geographic area
Pandemic - sudden, unexpected increase globally
Now remember that any measurement is always a measure of what has already happened. Customer satisfaction is a measure of last month's customer interactions, sales is a measure of last quarter's sales. These rear-view-mirror measurements are usually intended to inform what future we see out of the front windshield and R0 is no different. The problem in this case is that as this pandemic grows and more data is available, the numbers change. This means that we can't draw many conclusions based on the R0 value itself, but perhaps can understand it better based on the underlying variables.
In epidemiology, R0 expresses the average number of individuals in a susceptible population who will be infected by a contagious individual***.
If the R0 is less than 1 each infected person will, on average, infect fewer than one person which means the virus will die out on its own.
If R0 equals 1 each infected person will infect one other person. The virus will stay alive and stable, but there won’t be an outbreak or an epidemic.
If R0 is more than 1, each infected person will infect more than one susceptible person. So the virus spreads and there may be an outbreak or epidemic, or in this case a pandemic.
Now anyone who knows more about medicine or epidemiology than I do (there are a lot of them) may start picking apart my use of R0 and that's fair. But my point here isn't to talk about the relative benefits and drawbacks of the measure itself (there is a better discussion of that here). Instead my point is to use this example to talk about how critical it is to know the variables that make up any measure.
The variables in this case are
Infectious period - how long an infected person remains contagious. Part of the problem with COVID-19 is that reports vary on how long a person can be contagious. But evidence has shown that someone with few or no symptoms may still infect others.
Contact rate - the number of susceptible people with whom an infected person will come in contact. This is the whole reason for social distancing. While we're learning the infectious period, the length of time with the virus but without symptoms means the higher the contact rate the higher the immediate risk.
Transmission mode - whether through the air (the flu) or through bodily fluids (Ebola, HIV). We know that COVID-19 is transmitted through the air like any other flu virus.
Testing accuracy - While not a variable in the actual virus spread (and not in any of the definitions of R0 I read), it's important to call out COVID-19 testing accuracy anyway. All of the statistics that go into estimating R0 include the number of cases and number of cases is reliant on people with the virus getting tested. Because some people who are capable of passing on the virus may not show symptoms for up to two weeks, and some may never show symptoms. Additionally, states in the US are just now getting access to enough tests, so it's certain that there are contagious people in the world who have no idea they're infected.
| Estimated R0 values
COVID-19 - 1.32**
SARS - 3
H1N1 - 1.5
HIV - 4
Measles - 18
COVID-19 R0 is estimated at 1.9** based on early analysis done on cases in Wuhan, China between December 2019 and January 2020, although it's likely that we won't know the final R0 value until after the pandemic is under control.
*Because I'm a perfectionist and this website text editor doesn't make it easy to express "R naught" correctly throughout this text, I'll show you here that it should look like R0 when typed.
**Since beginning work on this blog post, the estimate changed from 1.9 in one study to 1.32 in another one, as more data was available.
***Limited evidence supports the applicability of R0 outside the region where the value was calculated
References:
Bates Ramirez, Vanessa. "What is R0?: Gauging Contagious Infections." Healthline.com, medically reviewed by University of Illinois-Chicago, College of Medicine, June 24, 2016, https://www.healthline.com/health/r-nought-reproduction-number#rsubsubvalues
Delamater, P. L., Street, E. J., Leslie, T. F., Yang, Y., & Jacobsen, K. H. (2019). Complexity of the Basic Reproduction Number (R0). Emerging Infectious Diseases, 25(1), 1-4. https://dx.doi.org/10.3201/eid2501.171901.
Du Z, Xu X, Wu Y, Wang L, Cowling BJ, Ancel Meyers L. Serial interval of COVID-19 among publicly reported confirmed cases. Emerg Infect Dis. 2020 Jun [cited March 30, 2020]. https://doi.org/10.3201/eid2606.200357
Porter, Kelly A., Tuel, Kelley R., "Have You “Herd”? Modeling Influenza’s Spread", CDC Science Ambassador Workshop 2014 Lesson Plan, 2014, https://www.cdc.gov/careerpaths/scienceambassador/documents/hs-have-you-herd-modeling-influenza-2014.pdf
