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The Banff International Research Station will host the "Challenges in Mathematical and Computational Modeling of Complex Systems of Substance Use, Use Disorders, and Related Problems" workshop in Banff from December 1, 2019 to December 6, 2019. Substance use disorders remain a top public health problem, with approximately 16 million adults in the United States having an alcohol use disorder (AUD). The range of problems associated with substance use range from acute and physiological (e.g., a hangover), to violence-related (e.g., child abuse), to mortality (e.g., overdose). According to CDC 2016 data, deaths from drug overdoses have doubled in last decade, with more than 60,000 deaths every year. We propose to bring together substance use modeling experts to identify critical challenges in its control and jointly develop the next wave of models that can properly address the complex dynamics inherent in its social systems. These models will examine phenomena at multiple scales to address the emergence of collective behaviors that arise from individual elements or parts of a system working together. Unlike biomedical and engineering problems, social systems present unique challenges. These include the need to assess impacts of policies, the long time scales often involved, the interdisciplinary nature of tackling these problems, the complexity of developing reliable models of human behavior, and the great difficulty of experimental testing. Successful change in social systems requires the active participation of a wide range of people in the modeling and policy design process. As applied to substance use, computational and mathematical models serve two essential purposes in efforts to reduce alcohol drinking, illicit drugs use and related problems within community environments. First, they clarify and direct empirical inquiries into the ecological circumstances and determinants of substance abuse behaviors and related problems. Second, computational and mathematical models can identify mechanisms of critical channels that encourage its use and can provide a coordinating framework for developing recommendations for comprehensive preventive interventions at the community level that are specific to problems and interests of community members. The development of computational and mathematical models is a vital step in advancing substance use preventive intervention research. Absent experimental methods, it is essential to build and test such models in order to develop realistic assessments of preventive intervention impacts in natural settings. Rather than assume independence among prevention strategies and their effects one-from-the-other, many of the existing computational and mathematical models enable us to account for system dependencies among the functional processes that underlie alcohol use. Previous mathematical models of social problems, which have been limited so far, have exhibited some critical aspects but have had key flaws (e.g., they considered these static processes or otherwise generated suboptimal responses to real phenomena). There is a need to address critical issues in complex social systems (e.g., how social dynamics evolve under disparate ecological and environmental conditions). In this workshop we will primarily focus on modeling methods to understand the spread and control of substance use and related problems (such as violence and intimate partner violence). The novel data-driven models will be designed and analyzed for pressing research questions in the field using methods from dynamical systems, agent based modeling, stochastic processes, operations research, and statistical techniques besides highlighting the type of data sets that may be needed to estimate parameters of such dynamic models. One substantive concern in this regard is the absence of adequate data on selection of substance use contexts, the reciprocal relationships of selection on substance abuse, and social mixing and influences that take place among high-risk individuals and abstainers in those locations. Sources of data and data visualization methods will also be discussed, as will statistical methods to connect the parameters of mathematical and computational models to these data. The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada-s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta-s Advanced Education and Technology, and Mexico-s Consejo Nacional de Ciencia y Tecnología (CONACYT).