Here in northern Kentucky, St. Elizabeth Healthcare, a regional hospital system, confirms up to 10 new cases of hepatitis C daily, said Deborah Henson, an infection control practitioner. Each positive test result starts a chain of events now all too familiar: St. Elizabeth reports it to the Northern Kentucky Health Department, which tracks down infected individuals to investigate how they contracted the virus and to try to keep them from spreading it. Some continue sharing needles and abusing drugs, while others make their way to hepatitis specialists whose caseloads are exploding.

They often learn that their insurance, if they have any, will not cover the treatment — highly effective new drugs cost at least $84,000 for a typical 12-week course. The cost of the new hepatitis drugs is so high that state Medicaid programs and many private insurers say that even treating a fraction of the infected population is breaking the bank.

Last year, Kentucky spent more than $50 million, about 7 percent of its total Medicaid budget, providing two of the new hepatitis C drugs, Sovaldi and Harvoni, to just 861 people, said Dr. John Langefeld, chief medical officer at the state’s Department for Medicaid Services. Sovaldi has a list price of $84,000 for a typical 12-week course of treatment; Harvoni, made by the same company, Gilead Sciences, has a list price closer to $100,000. Gilead offers discounts to Medicaid programs, but “it doesn’t do much to offset the significant cost factor,” Dr. Langefeld said.

In all, about 16,000 Kentucky Medicaid beneficiaries had a diagnosis of hepatitis C last year, up from 8,000 in 2013. That partly reflects the expansion of Medicaid under the Affordable Care Act to include more low-income adults, Dr. Langefeld said. But the state’s opiate problem, and increased testing of people who have injected drugs, are also factors, he and other health officials said. Kentucky will soon start providing hepatitis C tests at all its county health departments, just as it does for H.I.V.

Medicaid beneficiaries here are covered by private managed-care plans, each with its own rules for who can get the new hepatitis drugs. But patients generally need proof of Stage 3 or 4 fibrosis, or scarring of the liver, and cannot have used illicit drugs for at least six months, Dr. Langefeld said.