Iowa State researchers develop mathematical models which track and forecast COVID-19 spread throughout Iowa, the United States and the world

Data reveals that COVID-19 spread continues throughout Iowa and signals that social distancing has reduced transmission rates

A team of researchers in the Department of Statistics at Iowa State University has developed an extended varying coefficient SEIR (Susceptible Exposed Infectious Recovered) model for calculating COVID-19’s effective reproduction number (R). Epidemiologists agree that R values reveal critical characteristics of a virus—such as how contagious it is and how rapidly it is spreading through a population.

“We believe that our team has developed an accurate and reliable way for modeling the epidemic spread of COVID-19,” said Yumou Qiu, assistant professor of statistics at Iowa State University, and member of the research group. Yumou Qui “Our very detailed methods calculate those critical reproduction numbers, providing rich insights into how COVID-19 behaves and impacts targeted populations.”

Why the effective reproduction number (R) is a critical and reliable predictor

The R estimates the average number of people who will be infected with a disease from one contagious person, within a given population.

Researchers at Iowa State have calculated the effective R values. They’ve also modeled R0, pronounced “R-naught,” values which measure disease reproduction during the initial onset of an outbreak.

An effective R number reveals how contagious COVID-19 is for a specific population, each with its unique demographics and response policies. An R above 1.0 indicates that a disease is spreading; an R below 1.0 suggests that spread is decreasing and under control. 

“We know that the current R in Iowa is different from the R in New York city,” Qiu said. “R rates vary across countries, regions, states and even communities—because of many factors, such as population density, socioeconomic data—as well as national, state and local government responses to the spread of COVID-19.”

“The majority of our team’s predictions are based on the current trend of effective reproduction numbers,” he said. “Our models estimate infection and recovery rates for each day, using the data from neighboring days.”  

What the Iowa State models reveal about specific populations:


Similar to how meteorologists use models to analyze and predict weather patterns—Iowa State researchers created models to produced data-informed insights that explain the spread of COVID-19 in Iowa. Their models also reveal current COVID-19 transmission rates. Their analysis also sheds light on how Iowa’s current government policies may impact the spread of COVID-19

The group finds that Iowa’s effective R value peaked at 3.91 on March 16. When the first cases of COVID-19 were discovered in Iowa, in Johnston County, the estimated R0 value was 3.45.

By delving into the data, these statisticians extracted the story of how COVID-19 spread during the time that Iowa’s public schools, colleges and universities released students for spring break.

“That peak, or spike, in Iowa’s R value signifies a time when there was a lot of movement and activity around the state,” Qiu said. “Iowans were traveling in the state, college students were returning home and many people were departing and returning from vacation locations from across the globe.”

The data also reveal that Iowa’s current R is 1.65, a 50% drop from the March 16 peak of 3.91.

That’s good news, with a major caveat.

Although a 50% drop is encouraging, Qiu notes that an R value greater than one signals a compelling reality: that COVID-19 continues to spread across Iowa and continued spread fosters new infections that will continue to increase the number of infection in Iowa.

“These dynamics indicate that we have not fully controlled the spread yet,” he said. “We estimate that there are 741 undiagnosed COVID-19 cases in Iowa, and that this week’s confirmed infections will range from 680-1397.

Iowa Gov. Kim Reynolds declared a statewide public health disaster emergency on March 17. Since that date, the R has dropped significantly, falling from a 3.91 peak, to an all-time low on April 3 of 1.54.  Since then, Iowa’s R has trended slightly upward to its current value of 1.65. 

Iowa’s average R value during the last 10 days was 1.66, a further indication that infected Iowans continue to spread COVID-19 to others.

Qiu notes that the group hasn’t predicted future peaks or when COVID-19 will be eradicated in Iowa. This is due to uncertainty and  fluctuations in Iowa’s R values. 

“We don’t know when an infection will end. Those realities are sensitive to average recovery days and future infection rates, which can change rapidly. This is a very dynamic situation,” Qiu said. “Social distancing has made a significant impact in Iowa to slow the spread, but Iowa’s battle with COVID-19 continues to develop and change rapidly.”

United States

According to the group’s model’s, COVID-19’s R value in the United States reached a peak of 6.1 on March 11. It’s fallen to 1.1, with a recent 10-day average value of 1.32.

“This indicates that social distancing measures have been very effective,” Qiu said.

However, Qiu circles back to the realities of R values that are greater than one.

“The population of the United States is very high. This means we have a very large infection base,” said Qiu. “The combination of a large population and an R value above one indicates that the U.S. outbreak will continue to worsen.”

The numbers reveal a challenging road ahead for the United States. Qiu and his team estimate that 165,000 COVID-19 cases remain undiagnosed within our borders, and that 217,000–233,000 COVID infections will be confirmed this week.

The group also predicts that U.S. COVID-19 cases will peak mid- to late-April. They also forecast that case counts will fall during the summer, and that final accumulative confirmed cases with reach 1.2 million to 1.5 million in the United States.

“Just like Iowa, the national situation with COVID-19 is highly dynamic and volatile,” Qiu said. “How this virus runs its course and finally ends is sensitive to the average recovery day and the future infection rate. Many factors are at play here and how we respond could shift the numbers.”

Around the globe

The group has created models that reveal transmission patterns for European countries including: Italy, Spain, Germany, France, Switzerland, UK, Holland, Belgium, Austria, Norway, Sweden, Denmark and Portugal.

“The R average peak value of these 13 European countries is 5.3 on,” Qiu said. “The average current R value for these European countries is 1.0. In addition, the numbers show that Italy has reached its turnaround point.”

Their data show that Asian countries have successfully reduced their R values. South Korea's R value has declined from the peak 5.8 on February to its current 0.05. With 38 consecutive days of less than 1 R values, South Korea shows a definitive declining pattern which indicates current control of COVID-19.

“Japan’s R registered below one on March 1, then rose above one on March 17,” Qiu said. “Similar fluctuations are observed in Singapore, Portugal and Holland, signaling that those countries do not have control of the spread.”

Ongoing COVID-19 research at Iowa State University

This research team, housed in the Department of Statistics on the Iowa State University campus, includes members from several countries who collaborate across the globe. Team members include: Yumou Qiu of Iowa State University; and Haoxuan Sun, Han Yan, Yaxuan Huang, Xinyu Zhang, Ziheng Zhang, Yuqing Wang, Mengdi Shi, Jia Gu, Xiangyu Zheng, Yuru Zhu, Li Chen and Song Xi Chen from Peking University.

The team will continue to provide analysis and forecasts that are pertinent to Iowa, the United States and countries all over the world.

“The R numbers continue to be very important in gauging how well people—from Iowa to Europe and Asia—are responding to this global pandemic and if COVID-19 is spreading or under control,” Qiu said. This research is important because it can help policy makers determine what strategies are working and when more needs to be done to mitigate this global pandemic.”