Model How R naught (R₀) Shapes an Epidemic

Abstract

Even during a global pandemic like COVID-19, there are differences in how the epidemic unfolds within communities. Some communities see early, large waves of infected individuals, while others see smaller numbers of infections over a longer period of time, and others may not appear to have an epidemic at all. Could R₀ (pronounced R naught), account for some of this variation?

R₀, the basic reproduction number of a disease, 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. How much can differences in R₀ change the timing, intensity, and overall shape of an epidemic?

Start by working your way through the How R₀ Shapes an Epidemic Notebook in SimPandemic. When you get to the Sandbox portion of the Notebook, you can run your own simulations to explore questions like:

• Does lowering the basic reproduction number, R₀, change the timing and intensity of an outbreak?
• What effect does raising the basic reproduction number, R₀, have on the timing and outcomes of an outbreak?
• Research the basic reproduction number of other diseases, like influenza, polio, or measles. What would the epidemic have looked like if COVID-19's R₀ range was like one of those diseases?

When comparing the different simulations you run, consider looking at parameters like:

• On what day does the outbreak pass 1000 simultaneously infected individuals?
• What is the peak number of simultaneous infections?
• When does the peak of the outbreak occur?
• How long does the outbreak last?
• What is the total number of individuals infected?
• Do hospitals exceed their capacity?

When analyzing the data, it is best to run each scenario multiple times and calculate an average. This is because in the simulations, just like in the real world, many events are based on chance (e.g., who infects who and when). The element of chance can lead to differences in the outcomes. Usually these differences are fairly small and the trend remains stable, but some factors, especially those involving just a few people, have a larger element of chance.

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