This post has been updated.

Law enforcement and public health authorities have said that attempts to curb the illicit use of  prescription opioids may have fueled increased use of heroin, which is generally cheaper and widely available on the street. Some even believe that drug cartels have taken advantage of government efforts to crack down on "pill mills" — which dispense prescription narcotics with few controls — by flooding the eastern United States with heroin.

But a study released Monday shows that one state, Florida, was able to slow the rise in  reduce deaths from both prescription opioids and slow the rise in heroin deaths, at least for a couple of years in the case of the street drug, by enacting laws to regulate pain clinics and enforcing them rigorously.

However, if that effort did help, it may have had only a temporary impact. Florida figures show that the number of fatal heroin overdoses surged in 2014 and that there were a substantial number in 2013 as well.

In 2010 and 2011, Florida passed laws that restricted pill mills' ability to dispense medications on site and followed up with the arrest and prosecution of people who violated the laws, according to the research, which was published online Monday in the American Journal of Public Health. That led, predictably, to fewer opioid prescriptions, less diversion of the pain-killing drugs to illicit use and fewer physicians who purchased medications like oxycodone.

But when researchers from the Bloomberg School of Public Health at Johns Hopkins University compared Florida with North Carolina, which passed no new laws, they concluded that Florida's effort had also slowed the growth in fatal overdoses caused by heroin. In 2011, the rate of heroin overdose deaths rose by 18 percent per month in North Carolina, but just 8 percent monthly in Florida. In 2012, North Carolina death rates rose 10 percent per month, while Florida's increased by 6 percent. By late 2012, Florida's death rate had leveled off to about the mean for the period 2003 to 2012.

"By strengthening the regulation of pill mills and by targeting providers whose practices contributed to prescription opioid misuse, Florida may have prevented overdose deaths from heroin as well as from prescription opioids," the team wrote. The research was led by Alene Kennedy-Hendricks, an assistant scientist in the Department of of Health Policy and Management, and Daniel Webster, a professor in that department.

They acknowledged that their findings about Florida's impact on deaths from prescription opioids are more solid. But Webster said that "what I think made us feel more confident in what we were seeing ... is that we saw some initial substitution to heroin, but then in a more delayed way ... we then see the protective effect." The heroin question needs more research, he said.

In 2013, which was after the period studied by the Hopkins researchers, 199 people who died from overdoses had heroin in their bodies, according to Florida medical examiners. In 2014, that number more than doubled to 447 deaths, setting a record for the state.

Webster said that without a direct comparison to North Carolina's heroin fatality statistics, it is difficult to determine whether the Florida rate for those two years rebounded and whether the pill mill crackdown's impact was temporary.

The sharp rise in Florida heroin fatalities during those two years parallels a big increase in deaths there from fentanyl, an extremely potent painkiller that dealers are combining with heroin, as well as a nation-wide surge in heroin deaths. Across the U.S., heroin deaths rose from 5,925 in 2012 to 8,257 to 2013 and 10,574 in 2014, according to the National Center for Health Statistics, suggesting an escalation of the epidemic use of that drug.

The number of U.S. deaths from prescription opioids, which had leveled off nationally between 2009 and 2013, jumped sharply to 18,893 in 2014, the data show.

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