U-M Math Model Determines Effectiveness of Masks, Social Distancing

Researchers at the University of Michigan in Ann Arbor have developed a mathematical model that allows public health officials to determine how various levels of lockdown affect the economy and the mortality rate of COVID-19.
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woman wearing mask while working
U-M researchers have developed a mathematical model that shows that wearing masks and social distancing would simultaneously reduce the mortality rate and the economic impact of COVID-19. // Photo courtesy of the University of Michigan

Researchers at the University of Michigan in Ann Arbor have developed a mathematical model that allows public health officials to determine how various levels of lockdown affect the economy and the mortality rate of COVID-19.

The factors that end lockdowns the fastest with the smallest loss of life are those that include the use of masks and social distancing in everyday life, according to U-M researchers.

The model also found that the U.S. might reach herd immunity about 200 days into the pandemic, compared to a potential 18-month timeline for a vaccine. The Centers for Disease Control and Prevention estimates herd immunity occurs when 60 percent of people have contracted the disease and recovered, thereby stopping its exponential transmission.

“There are some personal behaviors that affect the transmission of the virus, and if you combine a lockdown with people being more careful, all these things help with slowing the spread of the virus, which means our lockdowns can be shorter,” says April Nellis, a doctoral candidate in the U-M Department of Mathematics.

“We also found that if we predict the vaccine will take a year-and-a-half from the start of the outbreak to arrive – which might be a little conservative at this point – it is pretty likely that we might reach herd immunity earlier. Of course, the vaccine will be important because immunity fades over time, but we wanted to know, ‘Could this happen in a safe manner before the vaccine arrives?’ Our model says yes.”

The model combines epidemic dynamics and macroeconomic cost modeling to simulate the costs of COVID-19. It predicts the spread of disease based on the number of susceptible individuals, number of infectious individuals, and number of removed individuals, or those who have died, recovered, or are resistant to the virus.

It includes other factors including recovery rate, base mortality rate, rate of ICU admittance, interaction level between groups, timeline for a vaccine or cure, and proportion of the workforce that can work remotely, among other factors.

The model shows that when people use caution, there is less economic loss and lower mortality. It includes two levels of lockdown – one for those ages 65 and older who are more vulnerable, and those ages 20-65 who are less vulnerable – and the effect of each level on the economy.

“We’re taking these two populations and trying to determine the best level of lockdown for each of them that can reduce deaths, keep infection levels from becoming too high, and also help maintain our economic productivity during this time,” Nellis says. “In a way, our paper is an investigation into seeing how changing different parameters in this model can help us see how the virus evolves.”

The researchers say different levels of lockdown for different groups can protect high-risk individuals while allowing low-risk individuals to resume work. There are also economic benefits to incorporating herd immunity into models considering lockdown measures: it shows lockdowns could end earlier and people could go back to work before the arrival of a vaccine.

For example, if no one social distances or wears masks, herd immunity would be reached before the arrival of a vaccine. Lockdown would last 249 days for those ages 65 and older and 219 days for those ages 20-64, with a 10.67 percent loss of economic output and a death rate of 0.37 percent of the total U.S. population.

If the country can reduce transmission by 95 percent by wearing masks and social distancing, however, herd immunity would still be reached and lockdown would last 189 days for those 65 and older and 24 days for those ages 20-64. In this case, the economic output loss would be 0.16 percent, and total deaths would decrease by 30.47 percent.

The paper is posted online in preprint and is currently submitted for peer review. It is available here.

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