# New Math for HIV Patients

After years of being viewed as a certain death sentence, the human immunodeficiency virus (HIV) is now considered a chronic health problem that can be managed with medication. But the virus’ ability to mutate and become resistant to drugs makes charting a course of treatment tricky, so physicians disagree on the benefit of early and continuous intervention.

To determine how best to treat patients whose HIV has been diagnosed early, Drexel Professor of Mathematics H. Thomas Banks and William Neal Reynolds Professor of Statistics Marie Davidian have developed a model to predict how the virus progresses in people. “The model shows numerically the battle raging within people between the virus and their immune systems,” Davidian says. After infection, most HIV patients achieve a natural plateau at which their bodies control the amount of virus in their systems. Those with higher plateaus develop AIDS quickly, while those with low viral loads can live for years without the disease. That has led some physicians to advocate “drug holidays” for patients. Pulling patients off treatment from time to time would give them a break from the physical and financial cost of taking a mix of antiviral drugs, Banks says. Yet, others maintain fighting HIV early and often is the best way to control the virus.

“More precise targeting of populations and treatments has the promise to produce improved drugs and more effective uses.”

Banks and Davidian validated the model—a series of differential equations involving parameters to describe the disease—using five years of data from scores of HIV patients at Massachusetts General Hospital in Boston. They then created a probability distribution for the parameters to characterize how various populations react to infections and to treatment cycles that begin and end at different intervals. “This model has sophisticated math and sophisticated statistics,” Banks says. “Neither would have worked without the other.”

“The model shows numerically the battle raging within people between the virus and their immune systems.”

With a \$3.5 million grant from the National Institute of Allergy and Infectious Disease, the College of Physical and Mathematical Sciences professors have teamed with Mass General on a four-year clinical trial. With a systems approach, the model determined three treatment cycles to study. Some HIV patients will receive no medication, while others will stop taking their drugs after three or eight months. Data will be collected during the trial, scheduled to start this fall, to refine the model. The goal, Davidian says, is to get as close to personalized medical treatment as possible. An even larger aim is to change the way drug trials are run, Banks says. “Mathematical models are a useful tool to design clinical trials,” he says. “More precise targeting of populations and treatments has the promise to produce improved drugs and more effective uses.”

A mathematical model developed by Drs. Tom Banks and Marie Davidian is being used to design a drug trial to test various treatment strategies for HIV patients.

HIV virus.