Abstract:
The use of methamphetamine is rising faster than most other hard drugs such as cocaine and heroine. To date, mathematical models have not been used to explore the dynamics of methamphetamine use in a population. We propose five mathematical models that can predict and evaluate methamphetamine use: a compartmental model for rural areas, a compartmental model for urban areas, an optimal control model for rural areas, an optimal control model for urban areas, and a metapopulation model. Both the optimal control and metapopulation models are built by extending the proposed compartmental structures. We separate models for urban and rural regions due to differing community characteristics that effect the manner in which methamphetamine is brought into and distributed throughout populations. Similar to models for the spread of infectious diseases, the interaction between susceptible, using, dealing, and recovered individuals in our illicit drug using population acts as a mechanism for the spread of methamphetamine use in each of our models. Thus, we use many techniques from infectious disease modeling literature in the analysis of our models. We also consider several applications of our models to data on methamphetamine use from Hawaii and Missouri. Our models give several important insights to previously observed yet unexplained characteristics regarding the dynamics of methamphetamine spread and the distribution of its use throughout the United States.
