How R₀ Shapes an Epidemic

As soon as a new infectious disease, like COVID-19, is discovered, one of the first questions is "What is the R₀?". R₀ (pronounced R naught) is the basic reproduction number of an infectious disease. It quantifies how many people, on average, an infected person can infect. For example, an R₀ of 3 means that an infected person will, on average, infect three more people. R₀ is the measure of how spreadable the disease is.

Three factors contribute to the R₀ for an infectious disease:

1. The infectious period of the disease. This is the average length of time, usually measured in days, during which an infected individual is able to pass the infection to another person.
2. The mode of transmission of the disease. Diseases can be passed from one person to another in many ways, including through direct contact with bodily fluids like blood, droplet spray from coughing or sneezing, or in the case of airborne diseases, small particles that stay suspended in the air for minutes or hours, even after the infected person has left the area.
3. The contact rate between individuals. This is the most variable factor and depends on the population. In densely populated cities, individuals tend to have contact (interactions) with more people per day than in sparsely populated rural areas.

Since some of the factors, like contact rate, are variable, R₀ is often given as a range. The R₀ range for COVID-19 is still being assessed in different parts of the world. So far, COVID-19 is thought to have an R₀ around 3. Here, we simulate a COVID-19 outbreak starting with ten infected individuals and an R₀ of 3. The resulting graphs and table show that if no public health mitigation measures (like social distancing, masks, or closures) are implemented, a large portion of the population is quickly infected.

Using the "Zoom In" button, you can see that in this simulation, the number of people infected (blue line) shoots up quite quickly within the first 4-6 weeks. As the infected patients recover, the number of immune individuals (orange) also increases. The infection runs through over 95% of the population (total infected) in this simulation in less than 200 days. This leads to overwhelmed hospitals with more patients needing hospitalization than the hospitals have capacity for.

An outbreak is an unexpectedly high number of occurrences of a disease in a specific location and time. If an outbreak undergoes a sudden increase in the number of cases, it becomes an epidemic. Because R₀ is a measure of how much a disease can spread, it can be used to predict whether an outbreak will turn into an epidemic.

In the simulation above, where the R₀ was 3, the outbreak from the ten initial COVID-19 positive adults spread rapidly and became an epidemic. In this simulation, we look at what would happen if the R₀ was much lower, 0.9. Looking at the Total Infections in the table, it is clear that some or all of the initial ten COVID-19 patients passed their infection on to others, but the total number of people infected remained low. The infected (blue) line on the graph can just barely be seen when you zoom all the way in.

If the R₀ for a disease is less than or equal to 1, an outbreak of the disease cannot turn into an epidemic. With each infected person only infecting, on average, zero to one other person, the disease does not spread quickly and eventually dies out. This is exactly what you see in this simulation where the total number of infections is low, but the outbreak continues for a while.

If you ran this same scenario many times you would see that sometimes the disease completely dies out within a year, while sometimes the disease remains at very low levels in the population throughout the year. This slight difference is because the model, like real life, has an element of chance in it. In real life, with such a low R₀, there is a chance that an infected person does pass along the disease, and a chance that they do not. For each individual in the simulation, SimPandemic also applies this chance, which is why slightly different outcomes are possible. To get a full picture of the possibilities, it is a good idea to run simulations that involve elements of chance multiple times.

As discussed above, R₀ changes depending on local conditions, like the amount of contact between people. If the average R₀ is around 3, some communities will have much higher R₀ values and others will have much lower ones. How might differences in R₀ change how different communities experience COVID-19? Do the same number of infections occur in a year? Do the hospitals perform the same? What about the number of deaths in the community? See for yourself by running a few simulations.

Let's use an R₀ of the 3 as the baseline. You will compare all other scenarios to this one.

To get started, press the "Customize Settings" button.

• In Disease Characteristics, make sure the “Basic reproduction number, R₀” is set to 3.
• Click the “Done” button.
• Change the “Name for simulation” and “Description for simulation” to reflect the scenario you are testing.
• Click the “Run Simulation!” button.”

Run the simulation several (at least 3) times.

Next, set the R₀ to 2 and run another set of simulations (at least 3). Run a third set of simulations with R₀ set to 4.

Look at all of the graphs and the table that were created. The blue line on the graphs represents the number of daily infections.

• How does the shape of that line change as R₀ increases?
• Does the epidemic last for a longer time or a shorter time?
• Are more people infected per day or fewer?
• Does the peak of the infected curve occur sooner or later in time?
• How is hospital capacity affected?

Based on your explorations, how might different communities have different impressions of how urgent a COVID-19 epidemic is?