What is “R Naught”(R0)?
If you haven’t seen the movie Contagion, this pandemic may be your first exposure to the term “R naught” or R0. This is a concept in statistics, a field which can be tricky to visualize for even those who’ve studied it. But in my opinion, stats can be an extremely interesting field once you’ve gotten over that main hurdle.
The basic reproduction number (R0) of a disease is a statistical concept referring to the average number of people who will be infected by one person with the disease when said disease is new to a population. If you are infected with a disease with an R0 of 1, that means that you will likely give the disease to one other person, who will also likely give the disease to one other person.
The higher a disease’s R0, the larger each ‘generation’ of the disease will be compared to the last one and the faster it will spread through a population. As such, incredibly infectious diseases have very high R0 scores, such as measles with an R0 of 12 to 18. Different seasonal strains of flu will have different R0 scores, but they can range from 0.9 to 2.1. Ebola has an R0 of 1.5 to 1.9 while the common cold has a score of 2 to 3. COVID-19 has an R0 of 2.79, so every person with the virus will, on average, infect two or three people, who will in turn infect two or three people each and so on.
That said, R0 is specifically applicable when a disease first appears in a population, when no one is immune. Once a significant portion of the population has had the disease, it becomes harder for the disease to spread. There are fewer “paths” for the virus to take. After the disease has begun to spread, effective reproduction number (Re) becomes relevant. The Re of a disease is the R0 multiplied by the fraction of the population which can still get the disease, aka it is the average number of people who will be infected by one person after the disease is introduced. The Re starts out the same as the R0, but reduces as the outbreak goes on.
Should the Re of a disease become 1, the disease will become endemic. It will exist within a population at a steady amount without spreading exponentially or dying out, like the common cold. Should Re fall below 1, then each ‘generation’ will become smaller than the last until the disease peters out. This point where Re falls below 1 is referred to as herd immunity, when there are enough immune people within a population that a disease can’t spread uninterrupted, even if there remains some susceptible people within that population.
On a side note, herd immunity is why vaccination is so important for society as well as for individuals. Not everyone can safely receive vaccinations (those under two years old, those who are immunocompromised), but if 80 to 90% of the population are vaccinated, there won’t be enough susceptible people for the disease to reliably jump from one person to the next.
Given that we do not have a vaccine for COVID-19, we can only lower the virus’ Re by wearing a mask, self-quarantining, and practicing social distancing.
Popular Question
In these trying times, a few have asked why we don’t just go back to business as usual, let COVID-19 work it’s way through the population, and then everyone will be immune and the pandemic will be over. The UK government briefly considered encouraging non-vulnerable people to willingly expose themselves to COVID-19 in order to rapidly develop herd immunity. The problem with this approach is that it doesn’t take into consideration the high cost in human suffering and death.
First off, achieving herd immunity wouldn’t immediately make COVID-19 go away. Herd immunity just means that each ‘generation’ of the disease is smaller than the last because there aren’t enough susceptible people for the disease to jump to. For example, for diseases with very limited numbers of infected people in a population, such as with diseases with vaccines like chickenpox or rubella, the disease won’t be able to spread through the population and will die out before too many people can be infected. However, COVID-19 has significantly spread throughout our population. Even if 90% of our population were to magically develop herd immunity, there could still be tens of thousands of infected people within the remaining 10%. Even if each ‘generation’ is only half the size of the last, it would still take over ten ‘generations’ for the virus to disappear. Since the first of these generations would involve thousands of new infected people, that would put far too many in harm’s way.
Secondly, for herd immunity to COVID-19 to be achieved, somewhere between 60-85% of the population would have to be immune. Until a vaccine is developed, the only way for this vast majority of the population to become immune is to become infected. Depending on their age and other factors, there are many, especially the elderly and infirm, who have a high chance of dying if they catch COVID-19 (up to a 10% chance of mortality for those 80+ years old. There can also be long-term health complications that no one has been able to study yet.
Additionally, herd immunity assumes a completely homogeneous population with no additional considerations to the nature of social interactions. For example, people are most likely to interact with people within their age cohort; children tend to interact with other children, the elderly tend to interact with the elderly, etc. Because of this, each age range can be considered its own mini-population that the virus will spread through somewhat independently. This means that, in order to truly ensure the elderly are protected using herd immunity, it won’t be enough for that 60 to 85% to only be young people. Sixty to 85% of the elderly would have to be infected in order to ensure their safety. If up to 10% of this cohort would die from infection, then just letting the virus run its course would necessitate at least a few million people dying in the United States alone, which isn’t an acceptable death toll for a consciously-implemented public health plan.
Finally, the majority of people can survive a COVID-19 infection, but some will only survive with medical intervention such as a respirator and possibly with other complications. If this pandemic were to run its course naturally, everyone in this group would get sick at once and hospitals would not be able to care for all of them. But if the coronavirus spreads slower, fewer people will be infected at once. This is what ‘flattening the curve’ refers to; the number of people who will ultimately be infected with the coronavirus won’t be greatly reduced (some estimates say it will reduce the total percentage of the population ultimately infected from 90% to 75%), but the virus will spread through the population over the course of a few years instead of over a few months, which is easier for the healthcare system to manage. Everyone who gets infected could receive the care they need to recover and almost all of them would survive.
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