Scalable Mathematical Models for Substance Use: From Social Networks to the Whole Populations Georgiy V. Bobashev, William A. Zule, Elizabeth D. Root, Wendee M. Wechsberg, Andrei V. Borshchev, and Alex E. Filippov. The College on Problems of Drug Dependence 66th Annual Meeting, June 12–17, 2004, San Juan, Puerto Rico
Mathematical modeling is a relatively new but fast developing area of substance use field providing researchers with additional dynamical dimension in epidemiological work and allowing scientists to simulate the consequences of various intervention and prevention scenarios. We illustrate these concepts by presenting two models. The first model describes Injecting Drug Users (IDU) networks, injecting behavior and HIV spread among the networks. The size, structure of the networks as well as frequency of injecting and HIV risks were obtained from published literature on urban IDU networks. This individual-based model was used to investigate the impact of introduction of Integral-cannula syringes (ICS) instead of commonly used Detachable Needle syringes (DNS). Laboratory experiments have shown that ICS retain about 1000 times less residual blood (<.001 mkl vs. 1 mkl) following injection and rinsing and thus provide about 100 times less risk of HIV/HCV transmission after 2 rinses than the DNS. Through dynamical simulations we have shown that it is necessary to have about 80% of users to switch to the ICS in order to reverse the spread of HIV and it takes more than 93% of users to switch to these syringes to reverse the spread of HCV. These results are quite robust with respect to the network size and frequency of use. We show how these simulation models could be matched on the actual geographical maps and followed in space over the time. The second individual-based model simulates substance use events among the US population allowing to estimate prevalence and incidence. Initially limited to alcohol, tobacco and marijuana use the model is using published age-specific rates of initiation and quitting for these substances. Such models allow identification of critical data gaps and validated models that are based on robust estimates allow identification of the most sensitive parameters that influence the course of drug using behaviors, developing optimal and cost-effective prevention and intervention policies and practices.
A Simple Deterministic Model of Drug Use