# Factoring in the Deadly Math of Cancer

### Researchers are building complex mathematical models to understand cancer's evolution and how to treat it.

Durham, NC - Two Duke researchers are focusing on the deadly mathematics behind the mutated genes and damaged cells that drive cancer.

"Cancer is the end result of an accumulation of genetic mutations," says Rick Durrett, a professor of mathematics at Duke. "It can be boiled down into a series of probabilities of whether or not a cell will become mutated, whether the cell will get the correct combination of mutations to become cancerous, and at what rate the cancerous cells continue to divide."

Cervical cancer illustrates his point. Tumors on a woman's cervix develop from a series of mutations associated with chronic infection from human papillomavirus (HPV), which the Center for Disease Control lists as the world's most common sexually transmitted infection.

Epidemiologist Evan Myers, a professor of obstetrics and gynecology at Duke, has created models showing how screening or vaccinating for HPV affects the likelihood of an individual or group getting cervical cancer.

What's needed, Myers says, are better models of the disease's underlying biology.

That's where mathematicians such as Durrett and Marc Ryser, a visiting assistant professor in Duke's math department, enter into the cancer equation. Mathematical models can complement clinical and biological data of the tissue-level effects of HPV, Ryser says. He explains that the mutations and cellular dynamics of the virus are hard to observe and track in real patients, but mathematical models can simulate an infection's progress without sampling a single cell.

"With our model, we can calculate the probability of infected cells continuing to divide and mutate. We can run simulations to see how the disease spreads in an individual and how it could spread to a person's sexual partners," Ryser says.

In the future, he would like to combine these kinds of tissue-level HPV models with the models Myers is developing for entire populations. The models together may let clinicians see "what is possible biologically and if it consistent with what we see clinically," Myers says. "If the models match reality, we could start to use them to make predictions about what transmission or treatments look like in the real world."

Ryser presented his early models on HPV in January as part of a semester-long Duke seminar series called Modeling Cancer. The seminar, which Durrett hosts each week at noon on Friday in Physics 119, is set up so mathematicians from Duke and other universities can discuss their work and build collaborations with clinicians in the medical center. The talks can be viewed live or later online.

Ryser has been collaborating with Myers to learn about the biological issues of HPV and cervical cancer that clinicians don't fully understand, and to factor these into his models. One unresolved question is why more than 80 percent of sexually active women get HPV at least once, but less than 1 percent have problems with persistent infections.

"With mathematical models, we can get a better sense of what we can't see, like the cell of origin where mutations start or when they start," Durrett says. "It's really a different point of view than from doctors who see cancer when it has developed far enough for a patient to have symptoms."

The goal of modeling cancer is "not to design a model and then run off into 'math land' to make abstract calculations that have nothing to do with the real world," Ryser says. Even if mathematicians are able to design correct cancer models, a cure for HPV or cancer may remain elusive. But, Ryser adds, such models could help optimize treatment schedules or dosages, or help determine which individuals get screened or how often they do.

"We want to develop translational models for medicine," he says. "The models are a valuable tool for scientists and clinicians to explore the dynamics related to disease."