R0 for Determining the Spread of Disease

Some diseases spread like wildfire. Some don't. And some diseases just die out. How do we figure out which diseases are going to spread and which won't? There's a term for this, R0, pronounced R "nought."

Imagine a class of first graders. One arrives at school sick. This sick child's illness infects another child. The second child could then infect one child; the third child could infect another. A chain of infections could spread the illness through the entire class.

In epidemiology, this is what we call a disease with an R0 of 1. Each case leads to one new case.

Illustration highlighting infectious people in a crowd
Max Oppenheim / Getty Images


R0 is the basic reproductive number. It describes how many kids will get sick when one sick kid enters the classroom (the population) and all the kids are able to get sick (they are susceptible). It depends both on the disease itself and the interactions of the kids.

When the R0 is higher than 1, more kids are infected. A high R0 doesn't mean it is a more dangerous disease. A cold can have a high R0, while a rare but deadly disease can have a low value, less than 1. 

Now back to the classroom.

R0 Less Than 1

Imagine that, on average, not every child infected another child. The first child infects a second; the second, a third. However, maybe the third doesn't infect any. The illness would stop spreading.

This is what happens when R0 is less than 1. Kids might get sick at first, but the disease will peter out.

R0 Greater Than 1

Let's go back to the first child, now imagine this child infects two others, those two kids infect two each (four all together). In total, seven would be infected.

The last four could then infect two each, leading to 15 infections in total. Pretty soon, there would be a lot of sick children. This is what happens when R0 is 2 and no sick kid is kept home.


In real life, not everyone is able to catch the bug. Some kids may be vaccinated. Some will get sick and can't get sick twice at the same time. Some kids will have gotten sick, recovered, and are immune. We say that not everyone is "susceptible."

In ongoing outbreaks, the effective reproductive number (R) explains disease spread. This is the average number of secondary cases per case in a mixed population—the average number of kids that each sick kid infects in a population with susceptible and non-susceptible kids. (R increases with the proportion susceptible. R = R0x, or R is the product of R nought and x, where x is the fraction susceptible.)

The number susceptible will change during an outbreak, as more kids get sick and recover or are vaccinated. Mixing of sick, immune, and recovered kids may also not be uniform.

Herd Immunity

If the first kid entered a room full of kids who were immune, the disease would not spread. If almost every kid had been sick already and was immune, the disease wouldn't spread.

If 8 out of 10 kids were vaccinated, the disease probably wouldn't spread. The sick kid might not interact with the 2 out of 10 kids who could get sick.

We call this herd immunity. That is, the immunity of some kids protects other non-immune kids from getting sick. Effective herd immunity should result in an R nought of much lower than 1; each child should not get one other child sick.

If R0 is large, herd immunity protects only if many are immune. (Herd immunity threshold = 1 - 1/R0.) The larger the R0, the more kids need to be vaccinated.


Some people spread more illness than others, like an ill teacher who works with every kid. Outbreaks can be more complicated than R0.

Real-Life Examples

One of the most infectious diseases is measles, with an R0 between 12–18. Before measles vaccination, a child could infect 15 children in one classroom. Those 15 classmates could then each infect 15 schoolmates. Measles spreads fast. To avoid measles spreading, many would need to be vaccinated.

We can also estimate R0 from contacts. In a classroom, contact might be kids playing blocks and sneezing onto their hands, spreading infection. R0 value depends on this contact. It depends on how long illness lasts, how many contacts a kid has when ill, and how often an illness spreads during each contact. 

A Word From Verywell

Researchers and experts use R0 in the field of epidemiology to help predict disease spread. It's a statistical concept with real-life application, as it can help distinguish which diseases may spread quickly, which will spread slowly, and which may start to die out.

4 Sources
Verywell Health uses only high-quality sources, including peer-reviewed studies, to support the facts within our articles. Read our editorial process to learn more about how we fact-check and keep our content accurate, reliable, and trustworthy.
  1. Centers for Disease Control and Prevention. Complexity of the basic reproduction number. January 2019.

  2. Li J, Blakeley D, Smith RJ. The failure of R0. Comput Math Methods Med. 2011;2011:527610. doi:10.1155/2011/527610

  3. Department of Health and Human Services. Vaccines protect your community.

  4. Guerra FM. The basic reproduction number (R0) of measles: a systematic reviewLancet Infectious Disease. 2017;17(12). doi:10.1016/S1473-3099(17)30307-9.

By Megan Coffee, MD
Megan Coffee, MD, PhD, is a clinician specializing in infectious disease research and an attending clinical assistant professor of medicine.