With cancer treatment, when a drug is given may matter almost as much as which drug is used.
For years, melanoma researchers have faced a frustrating contradiction. Experiments suggested that periodically stopping certain targeted drugs might help keep resistant cancer cells in check. Yet when intermittent dosing was tested in patients, continuous treatment performed better.
A new mathematical study offers a possible explanation. Instead of repeatedly switching treatment on and off, the researchers found that a better strategy may be to hit the tumor hard at first, gradually reduce the dose, and then stop treatment without restarting it.
Drug resistance remains one of the central challenges of targeted therapy for melanoma. These treatments can be highly effective against tumors carrying certain mutations, particularly changes in the BRAF gene, but resistant cancer cells can eventually emerge and allow the disease to progress.
Using Mathematics to Balance Tumor Control and Treatment Toxicity
Researchers Anthony Zamora, Natalia Komarova, and Souvik Roy investigated whether mathematics could identify a treatment schedule that better balances two competing goals: suppressing the tumor while limiting the harmful effects of therapy. Their study was published in Mathematical Biosciences.
“Traditionally, oncology treatments follow fixed dosing schedules. Patients receive chemotherapy, immunotherapy, surgery, or other treatments according to predetermined protocols,” said Roy, an associate professor of mathematics at The University of Texas at Arlington. “However, through several of my lab’s previous studies on esophageal and colon cancer, we found that continuous and dynamically adjusted dosing therapies may work better in two important ways: controlling the tumor and reducing toxicity.
“Reducing toxicity is a major benefit for patients. It can lower out-of-pocket medical costs for families and reduce overhead costs for hospitals.”
Why Intermittent Melanoma Therapy Looked Promising
The idea behind intermittent therapy came from an intriguing observation in laboratory studies. Some melanoma cells that develop resistance to targeted drugs can become dependent on the presence of those drugs, a phenomenon researchers sometimes describe as “drug addiction.” Remove the treatment, and those resistant cells may grow less effectively.
That raised an appealing possibility. Periodically withdrawing treatment might disadvantage resistant cells while allowing therapy to be restarted later. But when researchers tested that idea in patients, the results pointed in a different direction.
In one randomized Phase 2 trial involving people with advanced BRAF V600 mutant melanoma, intermittent treatment with the targeted drugs dabrafenib and trametinib produced worse results across multiple measures than continuous treatment. Median progression-free survival was 8.5 months with intermittent dosing and 10.7 months with continuous treatment. The overall response rate was also lower, at 57% compared with 77%.
The new mathematical work suggests the problem may have been the cycling itself.
A Mathematical Model Finds a Better Dosing Strategy
Roy and his colleagues used optimal control theory, a branch of mathematics designed to determine the best sequence of decisions in a changing system. In this case, the system included drug-sensitive cancer cells, resistant cells, tumor growth, and the costs associated with treatment toxicity.
The optimal schedule did not repeatedly alternate between treatment and breaks.
“Our model projects the best possible treatment schedule while balancing tumor control and treatment toxicity,” Roy said. “Rather than producing a fixed dosing pattern, it suggests an optimal sequence that begins with full-dose therapy, transitions to an intermediate dose, and eventually discontinues treatment without restarting it.
“The idea is to aggressively target drug-sensitive tumor cells early and then taper treatment before discontinuing it, reducing opportunities for drug-resistant cells to emerge and undermine the therapy.”
Why Gradually Tapering Treatment May Work
The mathematics point toward a one-way progression: maximum treatment first, less treatment later, then none. The model does not recommend repeatedly giving resistant cells alternating periods with and without the drug.
That finding helps reconcile the apparently conflicting laboratory and clinical results. Resistant cells may indeed behave differently when treatment disappears, but exploiting that vulnerability could require a carefully changing dose rather than a simple calendar-based schedule of treatment breaks.
The broader idea is known as adaptive treatment. Instead of assuming the same dose should remain optimal throughout therapy, treatment can potentially change as the tumor and its competing cell populations change.
Tumors are not uniform collections of identical cells. Treatment itself can alter which cell populations survive and expand. A therapy that is effective early in the disease may therefore create different biological conditions later.
Mathematics Could Help Personalize Cancer Therapy
“Mathematical models allow clinicians to evaluate treatment strategies before they are tested in patients,” Roy said. “Our goal is not to replace physicians, but to provide computational tools that help guide treatment decisions and improve patient outcomes.”
The same mathematical framework could be adapted to other diseases in which treatment suppresses disease while also causing toxicity and changing the balance between sensitive and resistant cells.
The American Cancer Society estimates that about 112,000 people in the United States will be diagnosed with melanoma in 2026, and approximately 8,510 will die from the disease. Melanoma represents only a small fraction of skin cancers, yet it causes a large majority of skin cancer deaths. At the same time, melanoma death rates fell rapidly from 2013 through 2022, largely because treatments improved.
Reference: “Optimal melanoma treatment protocols: A bilinear control model” by Anthony Zamora, Natalia L. Komarova and Souvik Roy, 9 July 2026, Mathematical Biosciences.
DOI: 10.1016/j.mbs.2026.109764
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