To read the full-text of this research, you can request a copy directly from the authors.


Methamphetamine abuse in the state of California has become an epidemic, where the state has been battling to control the spread of methamphetamine abuse with little to no success in various regions. Special precursor laws have been placed in California to stop its production and spread of this pshyo-stimulant drug. However, the impact of these laws has done very little on the production and sale of methamphetamine and in some cases cause imports from Mexico to increase and become more organized. The majority of the prior literature focus has been on the effectiveness of law officials and drug distribution and there is a widening gap about the social nature and dynamics of methamphetamine abuse. Understanding the dynamics of spread of methamphetamine abuse as a function of changing social structure can help understand the key components for controlling its abuse. We develop a mathematical model that captures the dynamics of methamphetamine abuse spread in California where social influences may result in new methamphetamine abusers. The model stratifies the population into two sub-populations: at-risk and not-at-risk populations. The not-at-risk population is the feeder for at-risk population whereas at-risk population is further divided into susceptible , methamphetamine users, users under treatment, users incarcerated for possession, and temporally recovered individuals. We use the concepts from epidemiology relating to the spread of infectious disease and compute the methamphetamine reproduction 1 number (R 0), defined as the average number of new users generated by a typical user in a nave population. The various data sets include hospital discharge cases for metham-phetamine related diagnosis, methamphetamine possession arrests data and, Treatment Episode Data Sets (TEDS). The model assumes data for hospital discharge cases as the methamphetamine user population, the arrest data for arrest population and the TEDS data for users under treatment. These data sets are used for estimation of the model parameters. Uncertainty and sensitivity analysis were performed to capture the variations in the methamphetamine patterns. Our hope is that the study results will identify mechanisms responsible for increasing temporal patterns of methamphetamine abusers in California.

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the authors.

ResearchGate has not been able to resolve any citations for this publication.
Full-text available
Illicit drug markets vary organizationally and operationally in terms of things like the product being bought and sold, the community and population being served, the people engaged in the business, and the extent to which the market has matured. In this paper we use data from a survey of 1,367 law enforcement agencies to examine the characteristics and dynamics of illicit retail methamphetamine markets in U.S. communities. We describe the characteristics of those markets and we distinguish different types of communities in terms of the characteristics of their local meth markets. Despite finding similarity in the organizational and operational characteristics of methamphetamine markets in the U.S., we found variability in terms of the source of production of meth for the local market (local labs and importing from Mexico and other U.S. states) and the extent to which local police consider meth to be a local problem.
Full-text available
This article articulates a subcultural basis to the evolving popularity for different illicit drugs primarily based on empirical research in the United States, especially among inner-city populations. From this perspective, drug use emerges from a dialectic between drug subcultures with individual identity development. The prevailing culture and subcultures affect drugs' popularity by imparting significance to their use. Innovations, historical events, and individual choices can cause subcultures to emerge and change over time. This subcultural view provides insight into the widespread use of licit drug, the dynamics of drug eras (or epidemics), the formation of drug generations, and the apparent "gateway" phenomenon.
Full-text available
Methamphetamine (MA) is a potent psychostimulant drug whose abuse has become a global epidemic in recent years. Firstly, this review article briefly discusses the epidemiology and clinical pharmacology of methamphetamine dependence. Secondly, the article reviews relevant animal literature modeling methamphetamine dependence and discusses possible mechanisms of methamphetamine-induced neurotoxicity. Thirdly, it provides a critical review of functional and structural neuroimaging studies in human MA abusers; including positron emission tomography (PET) and functional and structural magnetic resonance imaging (MRI). The effect of abstinence from methamphetamine, both short- and long-term within the context of these studies is also reviewed.
Full-text available
Accuracy of results from mathematical and computer models of biological systems is often complicated by the presence of uncertainties in experimental data that are used to estimate parameter values. Current mathematical modeling approaches typically use either single-parameter or local sensitivity analyses. However, these methods do not accurately assess uncertainty and sensitivity in the system as, by default, they hold all other parameters fixed at baseline values. Using techniques described within we demonstrate how a multi-dimensional parameter space can be studied globally so all uncertainties can be identified. Further, uncertainty and sensitivity analysis techniques can help to identify and ultimately control uncertainties. In this work we develop methods for applying existing analytical tools to perform analyses on a variety of mathematical and computer models. We compare two specific types of global sensitivity analysis indexes that have proven to be among the most robust and efficient. Through familiar and new examples of mathematical and computer models, we provide a complete methodology for performing these analyses, in both deterministic and stochastic settings, and propose novel techniques to handle problems encountered during these types of analyses.
Full-text available
This article reviews quantitative methods to estimate the basic reproduction number of pandemic influenza, a key threshold quantity to help determine the intensity of interventions required to control the disease. Although it is difficult to assess the transmission potential of a probable future pandemic, historical epidemiologic data is readily available from previous pandemics, and as a reference quantity for future pandemic planning, mathematical and statistical analyses of historical data are crucial. In particular, because many historical records tend to document only the temporal distribution of cases or deaths (i.e. epidemic curve), our review focuses on methods to maximize the utility of time-evolution data and to clarify the detailed mechanisms of the spread of influenza.First, we highlight structured epidemic models and their parameter estimation method which can quantify the detailed disease dynamics including those we cannot observe directly. Duration-structured epidemic systems are subsequently presented, offering firm understanding of the definition of the basic and effective reproduction numbers. When the initial growth phase of an epidemic is investigated, the distribution of the generation time is key statistical information to appropriately estimate the transmission potential using the intrinsic growth rate. Applications of stochastic processes are also highlighted to estimate the transmission potential using similar data. Critically important characteristics of influenza data are subsequently summarized, followed by our conclusions to suggest potential future methodological improvements.
Full-text available
The transmission dynamics of influenza in tropical regions are poorly understood. Here we explore geographical variations in the reproduction number of influenza across equatorial, tropical and subtropical areas of Brazil, based on the analysis of weekly pneumonia and influenza (P&I) mortality time series in 27 states. The reproduction number (R) was low on average in Brazil (mean = 1.03 (95% CI 1.02-1.04), assuming a serial interval of 3 days). Estimates of the reproduction number were slightly lower for Brazil than for the USA or France (difference in mean R = 0.08, p < 0.01) and displayed less between-year variation (p < 0.001). Our findings suggest a weak gradient in the reproduction number with population size, where R increases from low population in the North to high population in the South of Brazil. Our low estimates of the reproduction number suggest that influenza population immunity could be high on average in Brazil, potentially resulting in increased viral genetic diversity and rate of emergence of new variants. Additional epidemiological and genetic studies are warranted to further characterize the dynamics of influenza in the tropics and refine our understanding of the global circulation of influenza viruses.
A precise definition of the basic reproduction number, R o , is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if R o < 1, then the disease free equilibrium is locally asymptotically stable; whereas if R o > 1, then it is unstable. Thus, R o is a threshold parameter for the model. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super-and sub-threshold endemic equilibria for R o near one. This criterion, together with the definition of R o , is illustrated by treatment, multigroup, staged progression, multistrain and vector-host models and can be applied to more complex models. The results are significant for disease control.
Objectives: From 1983 to 2008, the incidence of methamphetamine abuse and dependence (MA) presenting at hospitals in California increased 13-fold. We assessed whether this growth could be characterized as a drug epidemic. Methods: We geocoded MA discharges to residential zip codes from 1995 through 2008. We related discharges to population and environmental characteristics using Bayesian Poisson conditional autoregressive models, correcting for small area effects and spatial misalignment and enabling an assessment of contagion between areas. Results: MA incidence increased exponentially in 3 phases interrupted by implementation of laws limiting access to methamphetamine precursors. MA growth from 1999 through 2008 was 17% per year. MA was greatest in areas with larger White or Hispanic low-income populations, small household sizes, and good connections to highway systems. Spatial misalignment was a source of bias in estimated effects. Spatial autocorrelation was substantial, accounting for approximately 80% of error variance in the model. Conclusions: From 1995 through 2008, MA exhibited signs of growth and spatial spread characteristic of drug epidemics, spreading most rapidly through low-income White and Hispanic populations living outside dense urban areas.
Background: Methamphetamine is a serious illicit drug problem in the United States and globally. For decades, methamphetamine has been supplied to the illicit market through local clandestine manufacturing and trafficking. In the early stages, illicit methamphetamine was produced and trafficked by motorcycle gangs and Mexican criminal groups. Over time, local clandestine manufacturing increasingly contributed to the illicit supply and broader methamphetamine problem. This review examines the evolution of the illicit methamphetamine supply in the U.S. Methods: A review of the literature on methamphetamine production and trafficking was conducted. Information was obtained from numerous sources including governmental reports, books and academic articles. Results: Attempts to control the supply of methamphetamine have only led to short term disruptions in availability. Clandestine manufacturing and trafficking have undergone significant changes over the past several decades. Shifts in local production have regularly been counterbalanced by changes in production and trafficking from criminal organizations in Mexico. Transnational criminal organizations now control much of the methamphetamine supply in the U.S. and methamphetamine remains widely available. Conclusions: The supply of methamphetamine in the United States is dynamic. Producers and traffickers have adapted to control efforts and the problem continues. Control efforts focused on eliminating supply are limited at best.
Higher disease rates among ethnic-minority populations compared to Whites have been pervasive and persistent over time, and as methamphetamine (MA) use continues to penetrate ethnically diverse geographic regions across the United States, minority populations may be at increased risk for adverse MA-related health consequences, thus further contributing to poorer health among vulnerable populations. This study examines racial/ethnic differences in health status and health conditions among individuals who used MA. Data are from a natural history interview study of adult MA users (N = 512), half of whom received treatment for MA abuse, and a comparison group who had not received substance abuse treatment. Chi-square and logistic regression analyses examined differences by race/ethnicity in self-reported health status and morbidity, adjusting for age, gender, and health behaviors including MA use severity and tobacco use. Overall, back/neck injuries (27%), severe dental problems (26%), gunshot/knife injury (25%), and sexually transmitted diseases (STDs) (24%) were commonly reported. Racial/ethnic differences were observed for conditions including gunshot/knife injuries, hearing loss, and learning disabilities disproportionately affecting Latino populations, and asthma and STDs disproportionately affecting African-Americans. Results varied by whether treatment for MA abuse was received. Although poor health and morbidity were common overall, each ethnic group may be at higher risk for specific health problems. Health status and conditions in this MA-using sample are examined and discussed with reference to general population data. These findings may assist researchers and treatment providers in addressing health consequences of the increasing prevalence of MA use among minority populations. Understanding ethnic differences in health status among MA users may assist in developing interventions to target specific health care needs.
Methamphetamine (meth) is a major drug of abuse in California and several other states, particularly among criminal offender populations. Over the past decade, substance abuse treatment systems have had to adapt to and accommodate the increasing needs of meth users and, in California, deal with the impact of Proposition 36, which has resulted in a greater number of criminal offenders entering the treatment system. This study examines selected treatment performance and outcome indicators for California Proposition 36 offenders entering substance abuse treatment for meth use and compares their performance and outcomes to other subgroups of California treatment clients differentiated by whether or not they were admitted to treatment through Proposition 36 and whether or not their primary substance was meth. Significant improvements in all outcome domains were seen across the populations, and treatment performance and outcomes were not substantively inferior for the offender or meth-using groups.
Alcohol consumption is a function of social dynamics, environmental contexts, individuals' preferences and family history. Empirical surveys have focused primarily on identification of risk factors for high-level drinking but have done little to clarify the underlying mechanisms at work. Also, there have been few attempts to apply nonlinear dynamics to the study of these mechanisms and processes at the population level. A simple framework where drinking is modeled as a socially contagious process in low- and high-risk connected environments is introduced. Individuals are classified as light, moderate (assumed mobile), and heavy drinkers. Moderate drinkers provide the link between both environments, that is, they are assumed to be the only individuals drinking in both settings. The focus here is on the effect of moderate drinkers, measured by the proportion of their time spent in "low-" versus "high-" risk drinking environments, on the distribution of drinkers. A simple model within our contact framework predicts that if the relative residence times of moderate drinkers are distributed randomly between low- and high-risk environments then the proportion of heavy drinkers is likely to be higher than expected. However, the full story even in a highly simplified setting is not so simple because "strong" local social mixing tends to increase high-risk drinking on its own. High levels of social interaction between light and moderate drinkers in low-risk environments can diminish the importance of the distribution of relative drinking times on the prevalence of heavy drinking.
All-cause mortality among individuals
  • C Russell
  • James K Callaghan
  • Marina Cunningham
  • Jenna Verdichevski
  • Sykes Mmath
  • R Sukaina
  • Stephen J Jaffer
  • Kish
Russell C Callaghan, James K Cunningham, Marina Verdichevski, Jenna Sykes MMath, Sukaina R Jaffer, and Stephen J Kish. All-cause mortality among individuals
Monitoring drug epidemics and the markets that sustain them using adam ii: Executive summary
  • A Golub
  • H Brownstein
  • E Dunlap
A. Golub, H. Brownstein, and E. Dunlap. Monitoring drug epidemics and the markets that sustain them using adam ii: Executive summary. 2012.
Dynamics of Methamphetamine Markets in New York City: Final Technical Report to the National Institute of Justice
  • J T Wendel
  • B Khan
  • K Dombrowski
  • R Curtis
  • K Mclean
  • E Misshula
  • R Riggs
  • D M Marshall
J.T. Wendel, B. Khan, K. Dombrowski, R. Curtis, K. McLean, E. Misshula, R. Riggs, and D.M. Marshall IV. Dynamics of Methamphetamine Markets in New York City: Final Technical Report to the National Institute of Justice. John Jay College of Criminal Justice, 2011.