Math and Medicine Join Forces to Solve a Cancer Mystery

By applying mathematics to solve a long-standing cancer mystery, Rachel Sousa (left), Francesco Marangoni and John Lowengrub offer new hope for melanoma patients. Steve Zylius / UC Irvine

Irvine, Calif., Aug. 20, 2026 — Immunotherapy has transformed outcomes for many cancer patients. Unlike conventional treatments, these therapies do not attack tumors directly. Instead, they enable the body’s own immune system to identify and kill cancer cells that had previously escaped elimination.

For patients with advanced melanoma – a particularly aggressive form of skin cancer – PD-1 blockade immunotherapy has converted what were once terminal diagnoses into cases of long-term survival. Patients who respond successfully and remain cancer-free for three years have a greater-than-95 percent probability of living at least 10 more years. Unfortunately, favorable outcomes of this kind remain the exception. Approximately 7 out of 10 melanoma patients treated with PD-1 blockade immunotherapy experience disease recurrence, even when the treatment initially appeared to be effective.

Determining why immunotherapy loses efficacy – and identifying strategies to address that failure – has been among the most challenging problems in cancer research. It has also been among the most resource-intensive to investigate, as the conventional approach is both slow and incremental: Researchers typically design experiments to test one hypothesis at a time, a process that can span years and require substantial funding.

A research team at the University of California, Irvine pursued a different approach. Rather than testing numerous potential explanations sequentially in the laboratory, the members first constructed a mathematical model capturing the key interactions between tumor and immune cells and then used that model to identify the most probable mechanism of resistance.

Their findings were published in the journal Cancer Research.

“We integrated two entirely distinct disciplines – mathematics and biology – and enabled them to inform one another,” said Francesco Marangoni, a cancer immunologist, assistant professor of physiology and biophysics, and one of the study’s senior investigators. He collaborated closely with co-senior investigator John Lowengrub, a Distinguished Professor of mathematics, biomedical engineering and systems biology, as well as Rachel Sousa, the study’s first author and a graduate student researcher in the interdisciplinary mathematical, computational and systems biology program.

Read the full press release in UC Irvine News.