Olivia Prosper and team's mathematical framework would be adaptable to different disease systems and inform strategies to reduce the threat of resistant pathogens to global health.

A collaborative project led by a University of Kentucky professor is exploring how math can be used to better understand the spread of drug-resistant diseases.

Olivia Prosper, assistant professor of mathematics in the UK College of Arts and Sciences, is lead principal investigator of the $550,000 project funded by the National Science Foundation's Division of Mathematical Sciences. The study addresses the growing worldwide concerns over drugs becoming less effective as pathogens become more resistant.

The more people take certain drugs, such as antibiotics, the less effective they can become over time as the microbes evolve. Prosper and her team are developing mathematical tools to improve understanding of how these types of drugs behave within the body, and how this behavior can influence the spread of drug-resistant diseases.

"One of the challenges in developing this framework is coming up with a way to link the drug dynamics that occur within each human host to the transmission dynamics between a population of individuals, that operate at different time scales," said Prosper, who has an interest in applying mathematics to problems related to human health. "We have proposed a method to tackle this problem."

Prosper's team uses vector-borne diseases, such as malaria, as their benchmark example. By understanding the process, their framework can help guide drug development and dosing protocols to balance the immediate benefits of administering drugs to those in need with the long-term population risks associated with drug-resistance. Ultimately, their framework would be adaptable to different disease systems and inform strategies to reduce the threat of resistant pathogens to global health.

"Mathematics allows us to boil down a very complex biological problem into its most fundamental components," Prosper said. "Here, we use differential equations that describe how the system changes over time in response to different interactions or events. These interactions include contacts between healthy and infected individuals, changes in drug concentration within the body over time, changes in pathogen load within the body over time, and the response of the pathogen when it is subjected to a particular drug concentration."

The other principal investigators on the collaborative project include Katharine Gurski (Howard University), Miranda Teboh-Ewungkem (Lehigh University), Angela Peace (Texas Tech University) and Zhilan Feng (Purdue University). Carrie Manore, with Los Alamos National Laboratory, is senior personnel on the grant. The grant is also providing opportunities for graduate students at these institutions to intern at Los Alamos.