R0 Calculator

Welcome to the R0 Calculator

R0 is a term commonly used in epidemiology that helps to describe the rate of infection of a disease.

What is R0? (R Naught)

In epidemiology, the basic reproduction number or R0 (pronounced “R nought”) of an infection can be thought of as the expected number of cases generated by one case in a population where all individuals are susceptible to infection. 

Does R0 have a formula?

Yes and no. There are many ways to come to a conclusion on what the R0 of an infectious disease is, but there is a formula that epidemiologists use to find this number. R0 = S * L * β

What are the variables that make up the R0 equation?

S = Susceptible Hosts – This is the number of people an infected individual comes into contact with per day while infectious with a disease.

L = Length of Infection – The number of days that an infected individual is infectious to the people he comes into contact with.

β = Transmissibility – This is a number that quantifies the ability for an infectious agent to spread between people or from the agent hosts to people.

More About R0 & How It's Calculated

Is this calculation accurate?

Once again the answer is yes and no. There are many reasons why this formula might not result in a very accurate answer. Let’s explore a few.

  • The number of susceptible hosts will vary from infected person to person. Let’s take a recent example of COVID19. In South Korea, the first few infected individuals only came into contact with a small number of susceptible hosts, while the 6th individual came into contact with over 1200 individuals. This might result in two very different R0 calculations even though the R0 should be the same from person to person. Why?
  • The transmissibility of the disease will actually change from situation to situation and environment to environment. Let’s say that the 1st infected Korean came into contact with 52 individuals while infectious and was in close physical contact with each individual. Now let’s presume that the 6th individual, who came into contact with over 1200, contacted each person in an outdoor environment and never came into physical contact with anyone. The number of people who would eventually get infected from either one of those individuals is very different because the spread of the Novel Coronavirus is lessened without physical contact or within closed quarters where the airborne virus might spread through the air. The first person might have been more responsible for the spread of the disease than the other. While this was not actually the case, it does show how difficult it can be to judge an outbreak by a number.
  • Length of infection can vary from person to person. We still know very little about COVID-19, but we do know that certain risk factors can increase or decrease the likelihood of serious complications when battling this respiratory illness. We know from China, that elderly men who smoked were at much higher risk of death than any other demographic category in their country. Those at high risk who recovered spent more time being contagious than children, who showed little to no symptoms of the disease. This will always skew data and therefore makes this a difficult number to calculate.

If this calculator doesn't give me the best R0, where can I find it?

There are specific governmental bodies that publish data about infectious disease. They report cases, deaths, R0, mortality rate, and so much more. Please check them out for the most accurate data on infectious disease.

  1. Center for Disease Control and Prevention – CDC
  2. World Health Organization – WHO
  3. CSSE at John Hopkins University

Common FAQ about the R0 Calculator

R0 or R-naught represents the number of new infections estimated to stem from a single case.

R0 or R-naught is important because it helps us to determine if a contagion will continue to spread faster than we can contain it. An R0 under 1 means we can go back to normal life. An R0 over 1 indicates growth and spread of a contagion and society will be shut down.

R0 or R-naught is a messy number. It is formed from science, forensic investigation, complex mathematical models, and some guesswork by the scientists formulating the answer. This number can change from day-to-day and from location to location. For this reason R0 is complicated to say the least.

Scientists estimate that the R0 or R-naught of the COVID-19 outbreak to be between 2.2-2.3. This number does change from time to time and from place to place.