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Abstract

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.

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