By the numbers: How infectious measles and other diseases spread | Science News for Students

By the numbers: How infectious measles and other diseases spread

An R0 is one measure of how easily a disease can spread
Jul 8, 2019 — 6:45 am EST
a child with measles scratching their back

Measles is extremely contagious. And one number, or rather a range of them, sums up the risk of its spread.


Two diseases have dominated headlines in the past few months. Measles sickened at least 1,044 people in the United States between January 1 and June 13. The virus has shown up in 26 U.S. states. And in the African country of Congo, Ebola has racked up 2,084 cases since August 2018. Of those, 1,405 people have died. This outbreak has also spilled over into neighboring Uganda.

Those numbers are scary. But another number illustrates how contagious a disease is. Really, it’s a range of numbers. It’s called the basic reproduction number, or R0 (pronounced “R naught”). This ratio describes how easily an infectious disease can spread.

Revealing ratio

Every infectious disease has a basic reproduction number, or R0. This is the average number of people who would catch the bug from one infected person, in a population where no one is immune to the disease.

Each dot in this graphic represents a person who would catch the disease from an infected person. R0 is usually expressed as a range because the factors that go into this ratio vary depending on the time and place of an outbreak.

a graph showing different basic reproduction numbers for various infectious diseases
Credit: T. Tibbits; Sources: P. Fine/Epidemiol. Rev. 1993; S. Hay et al./Philos. T. R. Soc. B 2013; G. Chowell and H. Nishiura/BMC Med. 2014

If one person is sick in an unvaccinated population, R0 estimates how many others that person would infect, on average. Researchers can use R0 to estimate how big an outbreak may become. They also would use it to plan a response if terrorists had found some way to turn a disease into a weapon.

Every infectious event or outbreak has an R0. Three main variables go into calculating it. The first is how long people stay contagious once they’re infected (the number of days, for example). The second is how often an infected person is likely to come into contact with others on a daily basis. And the third variable is the likelihood of infecting those people. In turn, those variables are influenced by other factors. Those include the local environment and the average age of infected people. An R0 also can be affected by how closely people live to each other and things such as what public-health resources are available to them.

Killer calculations

Within epidemics, R0 can vary from country to country. If there’s more than one way to catch a certain disease, R0 also can vary between the transmission routes. That’s why when scientists talk about the R0 for a disease, they’re usually talking about a range of numbers.

For measles, that range is 12 to 18: One person is likely to sicken 12 to 18 others. That’s high compared to something like Ebola. There, one person may infect another 1.5 to 2.5 people.

That might seem surprising when you consider how many people Ebola has killed. But R0 measures how contagious something is, not how deadly it is.

Part of what affects this R0 is how a disease spreads between people. Measles can travel through the air. Ebola instead spreads through bodily fluids. So the odds of making contact with the Ebola virus is far lower.

David Smith is an epidemiologist, or disease detective, at the University of Washington in Seattle. “With measles,” he explains, “if you’re anywhere near someone with the disease, you could get it.” That’s why getting the measles vaccine is so important.

Researchers also can use the R0 to figure out what share of people needs to be vaccinated to prevent a disease from spreading. This is known as herd immunity.

For measles, generally 92 to 95 percent of a population needs to be vaccinated to reach herd immunity. Because Ebola has a lower R0 range, it also has a lower herd immunity threshold. Estimates suggest that only 42 to 63 percent of a population would need to be vaccinated to reach herd immunity against Ebola. Current vaccines are not 100 percent effective against all of Ebola’s various strains. Because of this, some researchers argue that the threshold may actually be higher — and that current vaccination efforts won’t get us there.

The Rrange is not perfect. Researchers described its flaws in the January 2019 Emerging Infectious Diseases. For one thing, people don’t always define R0 in the same way. So even researchers may misinterpret what it means. And R0 can’t tell you how well a vaccine or other control is working while an outbreak is underway. For that you’d need to look at another reproduction number, called R effective or Rt. This number changes during an outbreak.

Using R0 to describe an epidemic “isn’t great,” Smith acknowledges. The number assumes everyone’s immune system is encountering the disease for the first time and there are no vaccines. In an epidemic, that’s rarely true.

Measles’ high R0 shows why it’s good that there’s a vaccine. Before one became widely available in the 1960s, millions of people got the measles each year — and hundreds of them died.

Power Words

(more about Power Words)

average     (in science) A term for the arithmetic mean, which is the sum of a group of numbers that is then divided by the size of the group.

contagious     An adjective for some disease that can be spread by direct contact with an infected individual or the germs that they shed into the air, their clothes or their environment. Such diseases are referred to as contagious.

Ebola     A family of viruses that cause a deadly disease in people. All cases have originated in Africa. Its symptoms include headaches, fever, muscle pain and extensive bleeding. The infection spreads from person to person (or animal to some person) through contact with infected body fluids. The disease gets its name from where the infection was first discovered in 1976 — communities near the Ebola River in what was then known as Zaire (and is now the Democratic Republic of Congo).

emerging infectious disease     A disease that suddenly has begun infecting increasing numbers of people or other organisms and could increase dramatically, more so in the near future.

environment     The sum of all of the things that exist around some organism or the process and the condition those things create. Environment may refer to the weather and ecosystem in which some animal lives, or, perhaps, the temperature and humidity (or even the placement of things in the vicinity of an item of interest).

epidemic     A widespread outbreak of an infectious disease that sickens many people (or other organisms) in a community at the same time. The term also may be applied to non-infectious diseases or conditions that have spread in a similar way.

epidemiologist     Like health detectives, these researchers figure out what causes a particular illness and how to limit its spread.

factor     Something that plays a role in a particular condition or event; a contributor.

herd immunity     A term that refers to the idea that if most people within a population are immune to a disease, then they can’t spread it. This tends to protect most people who are not immune.

immune     (adj.) Having to do with the immunity. (v.) Able to ward off a particular infection. Alternatively, this term can be used to mean an organism shows no impacts from exposure to a particular poison or process. More generally, the term may signal that something cannot be hurt by a particular drug, disease or chemical.

immune system     The collection of cells and their responses that help the body fight off infections and deal with foreign substances that may provoke allergies.

immunity     The ability of an organism to resist a particular infection or poison by providing cells to remove, kill or disarm the dangerous substance or infectious germ. Or, when used colloquially, it means the ability to avoid some other type of adverse impact (such as firing from a job or being bullied).

infect     (adj. infectious) To spread a disease from one organism to another. This usually involves introducing some sort of disease-causing germ to an individual.

measles     A highly contagious disease, typically striking children. Symptoms include a characteristic rash across the body, headaches, runny nose, and coughing. Some people also develop pinkeye, a swelling of the brain (which can cause brain damage) and pneumonia. Both of the latter two complications can lead to death. Fortunately, since the middle 1960s there has been a vaccine to dramatically cut the risk of infection.

outbreak     The sudden emergence of disease in a population of people or animals. The term may also be applied to the sudden emergence of devastating natural phenomena, such as earthquakes or tornadoes.

population     (in biology) A group of individuals from the same species that lives in the same area.

range     The full extent or distribution of something. For instance, a plant or animal’s range is the area over which it naturally exists. (in math or for measurements) The extent to which variation in values is possible. Also, the distance within which something can be reached or perceived.

ratio     The relationship between two numbers or amounts. When written out, the numbers usually are separated by a colon, such as a 50:50. That would mean that for every 50 units of one thing (on the left) there would also be 50 units of another thing (represented by the number on the right).

strain     (in biology) Organisms that belong to the same species that share some small but definable characteristics. For example, biologists breed certain strains of mice that may have a particular susceptibility to disease. Certain bacteria or viruses may develop one or more mutations that turn them into a strain that is immune to the ordinarily lethal effect of one or more drugs.

threshold     A lower limit; or the lowest level at which something occurs.

transmission     Something that is conveyed or sent along. (in mechanics) In a liquid-fueled vehicle, the machinery used to transfer power from the engine to the drive wheels. (In medicine) To spread a disease or toxic agent.

vaccine     (v. vaccinate) A biological mixture that resembles a disease-causing agent. It is given to help the body create immunity to a particular disease. The injections used to administer most vaccines are known as vaccinations.

variable     (in mathematics) A letter used in a mathematical expression that may take on different values. (in experiments) A factor that can be changed, especially one allowed to change in a scientific experiment. For instance, when researchers measure how much insecticide it might take to kill a fly, they might change the dose or the age at which the insect is exposed. Both the dose and age would be variables in this experiment.

virus     Tiny infectious particles consisting of RNA or DNA surrounded by protein. Viruses can reproduce only by injecting their genetic material into the cells of living creatures. Although scientists frequently refer to viruses as live or dead, in fact no virus is truly alive. It doesn’t eat like animals do, or make its own food the way plants do. It must hijack the cellular machinery of a living cell in order to survive.