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The Math of Epidemics: Q&A with Dalin Li, PhD

Research Scientist Explains the Numbers Behind the Spread of COVID-19

How can epidemics spread so quickly among entire populations? The Newsroom asked an expert, Cedars-Sinai research scientist Dalin Li, PhD, to explain the math behind the spread of COVID-19. Li was the first author of a recent study that showed how just a few infected individuals who came to the U.S could have generated more than 9,000 COVID-19 (coronavirus) cases.

Newsroom: How can one person ultimately spread COVID-19 to hundreds or even thousands of people?
Li: This occurs because of two facts. First, SARS-CoV-2, the virus that causes COVID-19, is highly infectious. Second, since this is a new disease, most of the population is not immune to the virus. Also, a virus spreads in a population in an exponential way, which means the speed of spreading is proportional to the people already infected. As more people get infected, infection rates speed up. In the case of COVID-19, with a highly contagious virus and a vulnerable population, the combination leads to much faster spreading.

Newsroom: Can you give an example?
LI: Let’s build a highly simplified model that assumes every infected person can pass the virus to three other individuals. (The actual rate of COVID-19 transmission is not known.) Then each of those three individuals passes it to another three, and so forth, in a process that is, say, repeated 10 times, which is known as 10 "generations." In that way, the infections can grow from three in the first generation to nine more in the second generation, to 27 more in the third and so on. If we add up the infected individuals in all 10 generations, that original number of just three cases grows to 88,572. This is how exponential growth can overwhelm a vulnerable population.

Newsroom: How might changes in behavior affect these numbers?
Li: Let’s assume we can reduce the transmission rate by one-third with some preventive procedures, such as good hygiene and physical distancing. That would mean one person now passes on the virus to two rather than three people. In this instance, doing the math, 10 generations would add up to 2,047 infections—a huge drop from the 88,572 infections seen in the first example.

Newsroom: That seems incredible. How could such a modest change have such a big impact on the number of infections?
Li: It's all about the math. The figures highlight how public health efforts, such as physical distancing and good hygiene, can be effective in reducing the scale of the pandemic or "flattening the curve," and how many lives we may have saved by following those principles. These efforts are particularly important because we don’t yet have highly effective treatments or a vaccine against this virus.

Newsroom: Did your research address how changing a specific behavior might affect the spread of COVID-19?
Li: No. Our models were based on the assumption that preventive measures in general can reduce the transmission of the virus to a certain extent. We did not study the effectiveness of a specific measure.

Newsroom: Are you developing new mathematical models in response to the ongoing epidemic?
Li: Yes. We have been looking into whether temperature affects the spread of COVID-19, and if so, to what extent. We need to fine-tune many parameters for this model, though, so it is an ongoing work.

Newsroom: What else do you think the public should know about the mathematics of the epidemic?
Li: A large proportion of infected individuals do not have disease symptoms. We still don’t know the exact figure. This situation makes it harder to control the spread of the virus. It points to the potential positive effect of the public following physical distancing rules even as we are reopening the society.

Read more in Discoveries: The Race to Develop a Vaccine for COVID-19