Drugs and maths seem an unlikely scientific combination. However, the two have been combined very effectively by a mathematician to give a picture of the actual number of drug addicts in Dublin.
Dr Catherine Comiskey explains that any number of real life situations can be modelled on maths.
"Algebra, sums, trigonometry, all can be applied to the real world, except that people usually think of things to do with the physical world, such as speed, cars, rockets, but it can be applied in any area, including medical and social applications. Anything that is changing in time can be applied in mathematics."
What the mathematician needs to look at, she says, is what affects that change, and then how to measure the elements that affect it.
"What affects the change in the numbers of people with HIV? There are a number of factors, including age. With an infectious disease affecting children, it could be the birth rate. With a bloodborne disease it could be the number of people sharing needles or the number of sexual partners. You measure those things and you build them into the model." Dr Comiskey, lecturer in mathematics and statistics at NUI Maynooth, was commissioned by the Department of Health to estimate, and she stresses that it is an estimate, the number of opiate users in Dublin.
In the past, she says, various agencies, such as the Department of Health and the Garda, did not share information on the contacts they had with people using drugs.
The Garda research unit produced a report of the number of records where drug use was noted in 1996 within the Dublin metropolitan area. The figure was more than 4,000. At that time according to the methadone treatment list there were over 3,000 people receiving methadone.
"The big question was whether those 3,000 were the same as those the police had. Did we have 4,000 in total or 7,000? Nobody knew because there is no information sharing."
Dr Comiskey also looked at the number of people admitted to the five main Dublin hospitals that year where opiates were involved.
However, even at that point, there was a question mark over the people using opiates who had not come into contact with any of those three places. "My job was estimating the actual number of opiate users in Dublin in 1996. I got special permission from the Data Protection Commissioner to get that information, since I am independent of those agencies."
The information given was initials, date of birth and the postal district in which they lived. From that she discovered that there were 6,000 people who had come into contact with the services for those using opiates.
To find the "hidden" population she used a mathematical method called capture-recapture, which is generally used in ecological applications. Taking three different "captures" in Dublin, she started with the methadone list and crossmatched it with the Garda list, and then with the hospital records. Applying the mathematical criteria, she estimated the number of people.
"My overall estimate in Dublin in 1996 was between 10,000 and 14,000. Before that there was no idea, people on the street had thought that it might be around 10,000. The Health Research Board says in its annual report that there were generally about 3,000 on methadone treatment.
"This method has been criticised because there are certain assumptions made, but it is the recommended method by the EU agency responsible for this area," says Dr Comiskey, who is an invited expert on the European Monitoring Centre for Drugs and Drug Addiction.
She says that by using the term opiate users she does not necessarily mean those people who seek treatment, "not necessarily problematic users". She would include those who may be holding down jobs.
Because of her experience with the EU monitoring centre, she is able put the figures for Dublin in a European context. "We are not that high in comparison to Rome for instance, but per head of population, we would be one of the higher cities."
Her figures showed that 5 per cent of males in the 15 to 24-year-old group were using opiates. "That is why our figures are quite high. I have looked at the social factors since then, where they live and this re-confirms that opiate use is linked to deprivation."