Epidemiological models to assess heroin epidemic waves and treatment outcomes

Researchers have recognized, for more than half a century, the similarities between the modes of spread of drug use and those of infectious diseases. Such an assumption allows one to model the consequences of drug use and epidemiological indicators and, using available data, to make impact assessments of drug policies and short- and medium-term predictions of interventions, which modify visible and hidden aspects, such as prevalence and/or incidence to be estimated.
A crucial issue concerns models with "closed populations" or with "open populations." The former consider fixed populations, with no inputs (births, immigration, etc.), only deaths can occur, and allow only short-term predictions; the open population models, more complex, allow medium- and long-term predictions of policy interventions, providing information to decision-makers. Recent data on the visible consequences of heroin/opioid use (overdoses, emergency interventions, etc.) and Eurostat's recent European estimates of the rapidly growing heroin market (in Italy, over 64% growth between 2011 and 2019) show that a second epidemic wave of heroin use is currently underway. In contrast, in Denmark, as well as in Switzerland, there is definitely an 'endemic' behavior of heroin use, confirmed by the data on overdose deaths, which is very low in Denmark and decreasing for young people in Switzerland. The main cause of this is the so-called Heroin Assisted Treatment (HAT), used in Switzerland for more than 25 years, and in Denmark for more than 12 years, which can be called the antiprohibitionist approach to treatment. The dynamic model, shown here, mathematically demonstrates the effectiveness of HAT.