15. That's all you need to know about the measles. OK, that's not true at all. There’s no one weird trick that will give you a flat belly (besides lying face-down on something flat), and there’s no one weird number that explains measles epidemiology. But the basic reproduction number, or R_{0}, of a disease does shed some light on which diseases become epidemics and how we can keep them in check.

R_{0 }(pronounced "r-nought") is defined as the average number of people that an infected individual will infect while he or she is contagious, assuming that everyone in the population is susceptible to the disease. It’s a quick and dirty way to describe how likely it is for a disease to spread through a population. The basic use is as a threshold: if the R_{0 }of a disease is greater than 1, then the disease is likely to become an epidemic. If it’s less than 1, the disease will die out. The R_{0} of last year's ebola epidemic was estimated to be between 1.5 and 2.5. For measles, the number is much larger: between 12 and 18.

The basic reproduction number of a disease isn’t the only thing we take into account when we evaluate a disease’s risks. Measles is much, much more contagious than ebola, but its death rate is much, much lower, so it makes some sense that people are more frightened of ebola than the measles. Even so, people do die of the measles. Before measles vaccination was widespread, it killed more than 2 million people a year. Today, people rarely die from the measles in developed countries, and vaccination is a big part of the reason why.

Of course, determining R_{0} is far from easy. Bacteria and viruses don’t come with microscopic labels containing this and other pertinent information. Both mathematical models and empirical studies help researchers determine the number. There are a few main factors that go into the calculation (see these notes for more information): the transmissibility (how likely a susceptible person is to contract the disease if exposed), how often infected people come into contact with susceptible people, and the length of infectiousness. Measles can be transmitted for a number of days, while HIV can be transmitted for life. Even so, the R_{0} of the measles is much higher than that of HIV because it is so transmissible.

R_{0} tells us not only whether a disease is likely to become an epidemic but also, very roughly, what proportion of a population must be vaccinated to keep a disease in check: 1-1/R_{0}. Why? Let’s say the R_{0} of a disease is 3. If no one is immune to the disease, an infected person will infect an average of 3 people. But if 2/3 of the population is vaccinated, only 1 of the 3 potentially infected people will actually get the disease. This brings the effective R_{0} in the population down to 1, the threshold for whether or not the disease will become an epidemic. Of course, this is a coarse estimate, but it explains why diseases with high values of R_{0} require such high vaccination rates to establish herd immunity. If the R_{0} of measles is 15, then we need about 14/15 of the population, or 93%, to be immune to the disease in order to keep it from (literally) going viral. Because the vaccine isn’t perfect, the vaccination rate needs to be even higher. If 10% of parents in an area choose not to vaccinate their children, the area may lose herd immunity and experience an outbreak.

That said, we should not put too much stock into the exact value of R_{0} for any given disease. Most R_{0} values are calculated after an epidemic and depend on the conditions of that particular epidemic. Did it occur in a region where people frequently come into contact with strangers? Was the weather conducive to survival of the pathogen? Did health care practices in the region exacerbate or mitigate the problem? The basic reproduction number isn't really attached to a disease but to a disease in a particular place and time. For example, a study of the 2014 ebola outbreak in West Africa found the R_{0} to be approximately 1.51 in Guinea, 2.53 in Sierra Leone, and 1.59 in Liberia. The same strain of the disease died out in Nigeria because the country implemented a successful program tracing exposed individuals and isolating them effectively.

A given outbreak of the measles is not guaranteed to have an R_{0 }between 12 and 18, and we cannot guarantee that with a 95% vaccination rate we will definitely achieve, or with a 90% vaccination rate we will definitely lose, herd immunity. But the basic reproduction number gives us an idea of the consequences of vaccination or refusal to vaccinate. Now might be a good time make sure you and any kids you might be responsible for are caught up on those shots.