Mathematical Models for Estimating Illegal Drug Use

In a climate of significant problem drug use opiates continue to be the main problem drugs. Illegal drug use is a hidden phenomenon, making it difficult to obtain accurate estimates of untreated use. Yet viable methods to produce current and regular prevalence and incidence estimates are required by policy makers and service providers responsible for allocating increasingly scarce resources. Using Irish data on cases of clients presenting for first treatment, incubation period distributions describing progression to first treatment were fitted. This was then applied with new analytical solutions of the back calculation equation and a linear Volterra integral equation to estimate for the first time the untreated population of opiate users. Based on these models for estimating the hidden incidence an integral equation model was derived and solved to estimate the prevalence of opiate use. A partial differential equation a model was then derived to describe the geographic spread of opiate use in Ireland. The methods and solutions produced address the very real problem facing service providers and planners in tackling and providing adequate services for problem opiate use.