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The benefit of mathematical models in medicine

Theoretical modeling sounds like it has, at best, a distant connection to the day-to-day concerns of medical professionals who care for or research the needs of patients. But when I spoke recently with Noah Rosenberg, PhD, a population geneticist at Stanford and editor of the scientific journal Theoretical Population Biology, he pointed out that modeling can offer distinct benefits to those in medical fields like epidemiology and genetics.

“We see a lot of occasions in public discussions of areas like the spread of epidemics, the demography of aging populations, and big data analysis in genomics where part of the backdrop arises from theoretical population biology work,” Rosenberg said. “We hope to spread the word that there is a place for the kinds of theoretical and mathematical insights that can contribute to those important topics.”

Rosenberg noted that papers in the journal often span the divide between mathematics and biology, but they have a few things in common. In an editorial he published last month in the journal, Rosenberg describes an ideal study for the journal - namely that first, “the mathematical work is motivated by a genuine problem in biology, and there’s a need for theory to resolve the problem,” he said. Secondly, the mathematical work is substantial enough that it uncovers new potential relationships or new explanations for a phenomenon, and lastly, that the advances contribute to our understanding of biology - though some of the best papers in the field can also have a big impact on the field of mathematics, too.

When I asked him to talk about what that would mean for studies that touch on health research, he pointed me to a couple of fascinating papers. One is a paper by Shai Carmi, PhD, and colleagues that explains a new way to look at shared DNA strands between people in order to understand their relatedness and the amount of overlap in their genomes. This has implications for how we think about “the way in which genes descend within families, including genes that may be related to a disease.” It’s one of the journal’s most downloaded papers, Rosenberg told me.

The second is a study by Maciej Boni, PhD, and colleagues that incorporates how decisions that poultry farmers in Southeast Asia make about market conditions might affect the spread of avian influenza in their flocks. When avian flu is identified in a region, poultry flocks are usually culled. It’s an interesting example of how human behavior can affect disease dynamics.

Rosenberg noted that the studies and models that are able to incorporate human behavioral patterns are among the most interesting that he sees. Nailing down how people’s decisions affect the course of an outbreak is notoriously difficult, but like the avian influenza paper demonstrates, mathematical models make it possible to explore the consequences of different assumptions about these decisions.

Rosenberg says that it’s even possible to make mathematical models of cultural practices (like deciding not to immunize your children) and how they spread among groups of people. One public laboratory this interaction is currently playing out in is the measles outbreak that got its start at Disneyland in December. The outbreak topped 100 cases nationwide, mostly among families that refuse to vaccinate their children. “It’s the intersection between human behavior and dynamics of disease,” he said. “Putting those together in a mathematical model to predict what might happen is the kind of work that appears in Theoretical Population Biology.”

Previously: Stanford physician Sanjay Basu on using data to prevent chronic disease in the developing world and Facebook app models how viruses spread through human interaction
Photo by Woodley Wonderworks

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