Mathematics professor Christopher Kribs said using differential equations in math models can show how COVID-19 spreads through contact.

Differential equations describe how fast something changes by counting the number of people who are infected and the likelihood of new infections, Kribs said. Those new infections are what drives the outbreak.

Kribs’ main area of research, which did not previously focus on COVID-19, involves modeling vector-borne diseases like Malaria or West Nile. He has conducted research on contact tracing during quarantine and the effects of isolation and quarantine in an outbreak, among other things.

The infection process requires two people to come into contact, one who is infected and another who is not, Kribs said. The rate of new infections depends on the number of people infected and the number of people available by contact, which produces a new generation of cases through doubling time.

Doubling time is how long it takes for the next generation of infections to appear, which is around three days, Kribs said.

“The only thing that could slow this down is changing the number of people who are available to infect,” he said.

President Donald Trump extended social distancing guidelines Sunday with the expectation that the country will be well on its way to recovery by June 1. Local government officials, such as those in Arlington and Dallas, have followed suit and have extended their own guidelines and stay-at-home orders.

Distancing measures help reduce the amount of contact people may have with those infected, Kribs said.

“With no distancing practices going on, an infected person would potentially infect 10 people a week,” Kribs said. “Then the next generation is going to be 10 times as big a week later.”

In a scenario where distancing measures keep 80% of people at home, it will only cause two new cases a week later instead of 10, he said. Holding those measures in place makes a difference in the number of people possibly getting infected.

Social distancing helps to mitigate the transmissions for COVID-19, said Yuan Zhou, assistant professor in the Industrial, Manufacturing and Systems Engineering Department.

Zhou’s dissertation focuses on the spread of diseases in shopping centers, specifically human behaviors during the spread of diseases.

COVID-19 has unique characteristics, Zhou said, such as the ability to stay in the air for several hours and on surfaces for more than a day or two.

According to the Centers for Disease Control, the best way to prevent illness is to avoid exposure by maintaining a distance of at least 6 feet or staying home.

However, the effectiveness of social distancing depends on its magnitude and timing, Zhou said.

“We may fail to control the disease spread if [social distancing] is not implemented in an appropriate way,” she said in an email. “For example, we may see the epidemic curve [go] up again if the social distancing is lifted too early.”

Mathematics graduate student Mondal Hasan Zahid said an example of a virus spreading is having 10 matches and lighting the first one, the fire then goes from one match to another and continues. By removing a match in the middle, the remaining ones will not ignite.

“This is the actual idea about [social distancing],” he said. “If you can remove somebody, then the remaining part is safe.”


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