In this section, we'll discuss another measure of transmissibility: Reproductive Numbers. We'll start by discussing the basic reproductive number. Now, the basic reproductive number sometimes denoted R sub 0, or R naught, is the number of people infected by a single infectious individual in a fully susceptible population. It's a basic measure of how transmissible a disease is. You'll think of this as illustrated on the right that a single infected person walks into a population where everybody else is susceptible. So I show up in a city, say New York City, I'm infected with a new disease, no one's seen it before, everybody is at risk. I infect four people, or at least on average, I'm expected to infect four people. Then the basic reproductive number for that disease is four. In contrast to the basic reproductive number, the reproductive number is the number of people infected by a single infectious individual in a population with immunity. Now, consider that situation before where I've come into New York and I'm infected with a disease, but this time instead of a brand new disease no one's seen before, this is a disease that circulated before, half the population is immune to that disease. So that means, of those four infectious events that I could have actually caused, if everyone's susceptible, only two of them will occur, because the other two potential infection events don't actually happen. So because half the people were immune and two out of four of the infectious events that could have happened didn't happen, the reproductive number or R, is equal to two. So as I just explained, the reproductive number is in most cases, equal to the basic reproductive number times the percentage of the population that's actually susceptible to infection. So the reproductive number has a very defined and constant relationship with epidemic curves, or the shape of the epidemic curves. At the start of the epidemic, if it's a brand new pathogen and no one's immune, the reproductive number is equal to the basic reproductive number. During the period when the epidemic is growing, the reproductive number is by definition greater than one. If you think about what the reproductive number means, this should be clear. If every time a person is infected, they are infecting more than one other person. In the next generation of infections, there will be more infections than there are in this generation because each one person is causing more than one other case. So then the epidemic will grow, hence R is greater than one. But at some point, the level of susceptibility in the population will get low enough that people will stop replacing themselves in the population. That is, everybody infected will infect less than one on average, other person, that means the reproductive number is less than one. Since there's less people in every generation of transmission, the epidemic will recede. Because the epidemic starts receding as soon as the reproductive number goes below one, it's not necessary that everybody in the population gets infected. So at the end of the epidemic, some people will still be susceptible to the disease even though it dies out. So here's the basic reproductive number for some well-known diseases. You'll notice these ranges are pretty big. That's because the reproductive number is not just dependent on the disease itself, it's dependent on the context. So consider the first of these, cholera, where the basic reproductive number has been estimated to be between 2.5 and 15. Well, the reason the range is so big is because how cholera transmits is dependent a lot on sanitation, and the conditions for sanitation and water handling etc, in a particular place. If you're in a place where conditions are good enough, cholera won't even circulate. The basic reproductive number will be less than one. In places where cholera has circulated the conditions haven't been that bad, the reproductive number has been relatively modest, say around 2.5. But in places where the conditions were really conducive to the circulation of cholera and it could spread quickly, the reproductive number could be quite high, and has been estimated to be as high as 15. In general, the reproductive number though is relatively contained for particular diseases, and there is a surprising amount of consistency across settings. One of the diseases that would fit in the biggest ranges of reproductive numbers is malaria. Here, you'll notice that we say the range is between one and greater than 1000. That's because the ability for Malaria to transmit is very driven by environmental conditions, and people can stay infected with the parasite for a very long time. So if there's a lot of mosquito biting, and you stay infected with the parasite almost a year, and the environment is very conducive to transmission, a single person who causes as many as 1000 other cases. Let's go over some key points from this section. The basic reproductive number or R naught, R sub 0, is a core measure of disease transmissability. As I mentioned, R naught is a function of both disease and context. In populations with immunity, the number of people each case infects is the reproductive number, R. The value of R determines if this cases of disease are rising, declining, or stable during a particular epidemic. So here's an exercise to help you practice these concepts. If the basic reproductive number for cholera is three, what is the approximate percentage of the population immune when an epidemic starts declining? To answer this question, think a bit about: what is the reproductive number at different times in the epidemic? What is the relationship between the reproductive number are in susceptibility?
