Impact of Relative Residence Times in Highly Distinct Environments on the Distribution of Heavy Drinkers

Grounding alcohol simulation models in empirical and theoretical alcohol research: a model for a Northern Plains population in the United States

The growing number of systems science simulation models for alcohol use (AU) are often disconnected from AU models within empirical and theoretical alcohol research. As AU prevention/intervention efforts are typically grounded in alcohol research, this disconnect may reduce policy testing results, impact, and implementation. We developed a simulation model guided by AU research (accounting for the multiple AU stages defined by AU behavior and risk for harm and diverse transitions between stages). Simulated projections were compared to historical data to evaluate model accuracy and potential policy leverage points for prevention and intervention at risky drinking (RD) and alcohol use disorder (AUD) stages. Results indicated prevention provided the greatest RD and AUD reduction; however, focusing exclusively on AUD prevention may not be effective for long-term change, given the continued increase in RD. This study makes a case for the strength and importance of aligning subject-based research with systems science simulation models.

A review of mathematical modeling of addiction regarding both (neuro-) psychological processes and the social contagion perspectives

Addiction is a complex biopsychosocial phenomenon, impacted by biological predispositions, psychological processes, and the social environment. Using mathematical and computational models that allow for surrogative reasoning may be a promising avenue for gaining a deeper understanding of this complex behavior. This paper reviews and classifies a selection of formal models of addiction focusing on the intra- and inter-individual dynamics, i.e., (neuro) psychological models and social models. We find that these modeling approaches to addiction are too disjoint and argue that in order to unravel the complexities of biopsychosocial processes of addiction, models should integrate intra- and inter-individual factors.

Applying a complex systems perspective to alcohol consumption and the prevention of alcohol-related harms in the 21st century: a scoping review

BACKGROUND AND AIMS

A complex systems perspective has been advocated to explore multi-faceted factors influencing public health issues, including alcohol consumption and associated harms. This scoping review aimed to identify studies that applied a complex systems perspective to alcohol consumption and the prevention of alcohol-related harms in order to summarize their characteristics and identify evidence gaps.

METHODS

Studies published between January 2000 and September 2020 in English were located by searching for terms synonymous with 'complex systems' and 'alcohol' in the Scopus, MEDLINE, Web of Science and Embase databases, and through handsearching and reference screening of included studies. Data were extracted on each study's aim, country, population, alcohol topic, system levels, funding, theory, methods, data sources, time-frames, system modifications and type of findings produced.

RESULTS

Eighty-seven individual studies and three systematic reviews were identified, the majority of which were conducted in the United States or Australia in the general population, university students or adolescents. Studies explored types and patterns of consumption behaviour and the local environments in which alcohol is consumed. Most studies focused on individual and local interactions and influences, with fewer examples exploring the relationships between these and regional, national and international subsystems. The body of literature is methodologically diverse and includes theory-led approaches, dynamic simulation models and social network analyses. The systematic reviews focused on primary network studies.

CONCLUSIONS

The use of a complex systems perspective has provided a variety of ways of conceptualizing and analyzing alcohol use and harm prevention efforts, but its focus ultimately has remained on predominantly individual- and/or local-level systems. A complex systems perspective represents an opportunity to address this gap by also considering the vertical dimensions that constrain, shape and influence alcohol consumption and related harms, but the literature to date has not fully captured this potential.

Optimal control of alcoholism spreading through awareness over multiplex network

This paper proposes the SISRS epidemic model to represent alcohol addiction among people. The spreading of alcohol addiction is controlled by creating awareness among the people and also by treating them to overcome it. Multiplex network is used to study the dynamics of addiction. Alcoholism spreads over the physical contact layer and follows the SISRS process whereas human awareness spreads over the virtual contact layer and follows the UAU process. Based on the Microscopic Markov Chain Approach competing dynamics of spreading of alcohol addiction and human awareness diffusion are studied. Necessary conditions for the existence of an alcohol-free population are found. An optimal control problem using a suitable cost index is formulated to reduce the alcohol addicts and the optimal control strategy using Pontryagin’s Minimum Principle is determined. Numerical results are developed to find the effect of various parameters and to analyze the effects of different control strategies. The results obtained from this model are closer to the data collected in the National Survey of Drug Use and Health (NSDUH) from 2002 to 2018.

Threshold dynamics of a multi-group SEAR alcoholism model with public health education

In this paper, we investigate the threshold dynamics of a multi-group SEAR alcoholism epidemic model with public health education. The multi-group model allows us to describe interactions both within-group and inter-group separately. We prove that the basic reproduction number [Formula: see text] plays the role of a threshold for the long-time behavior of the model. The alcohol-free equilibrium [Formula: see text] of the model is globally asymptotically stable if [Formula: see text], while the alcohol-present equilibrium [Formula: see text] exists uniquely and is globally asymptotically stable if [Formula: see text]. For the proofs of main results, we use the classical method of Lyapunov functions and apply subtle grouping technique in estimating the derivatives of Lyapunov functions guided by graph theory. Our results expand the previous results which have been obtained in single-group models. Sensitivity analysis and numerical simulations are also performed to illustrate our results.

Role of imitation and limited rehabilitation capacity on the spread of drug abuse

Objectives

We formulate a mathematical model for the spread of drug abuse using non linear ordinary differential equations. The model seeks to investigate both peer influence and limited rehabilitation effects on the dynamics of drug abuse. Peer-influence is modelled through the mechanism of imitation and limited rehabilitation is described using a special treatment function. Center manifold theory is used to show that the model exhibits the phenomenon of backward bifurcation. Matlab has been used to carry out numerical simulations to support theoretical findings.

Results

The model analysis shows that the model has multiple equilibria. It has been shown that the classical \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}_a$$\end{document}Ra—threshold is not the key to control drug abuse within a population. In fact drug abuse problems may persist in the population even with subthreshold values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}_a$$\end{document}Ra. This was shown to result, in particular when, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document}ω, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta _1$$\end{document}η1 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta _2$$\end{document}η2 are high enough such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega >\omega ^*$$\end{document}ω>ω∗, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta _1>\eta ^*_1$$\end{document}η1>η1∗ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta _2>\eta ^*_2$$\end{document}η2>η2∗. The results suggest the need for comprehensive and accessible substance abuse treatment services to curtail drug abuse.

Electronic supplementary material

The online version of this article (10.1186/s13104-018-3574-4) contains supplementary material, which is available to authorized users.

Stability of a binge drinking model with delay

A more realistic binge drinking model with time delay is introduced. Time delay is used to represent the time lag of the immunity against drinking in our model. For the model without the time delay, using Routh-Hurwitz criterion, we obtain that the alcohol-free equilibrium is locally asymptotically stable if [Formula: see text]. We also obtain that the unique alcohol-present equilibrium is locally asymptotically stable if [Formula: see text]. For the model with time delay, the local stability of all the equilibria is derived. Furthermore, regardless of the time delay length, using comparison theorem and iteration technique, we obtain that the alcohol-free equilibrium is globally asymptotically stable under certain conditions. Numerical simulations are also conducted to illustrate and extend our analytic results.

On the Role of Imitation on Adolescence Methamphetamine Abuse Dynamics

Adolescence methamphetamine use is an issue of considerable concern due to its correlation with later delinquency, divorce, unemployment and health problems. Understanding how adolescents initiate methamphetamine abuse is important in developing effective prevention programs. We formulate a mathematical model for the spread of methamphetamine abuse using nonlinear ordinary differential equations. It is assumed that susceptibles are recruited into methamphetamine use through imitation. An epidemic threshold value, [Formula: see text], termed the abuse reproduction number, is proposed and defined herein in the drug-using context. The model is shown to exhibit the phenomenon of backward bifurcation. This means that methamphetamine problems may persist in the population even if [Formula: see text] is less than one. Sensitivity analysis of [Formula: see text] was performed to determine the relative importance of different parameters in methamphetamine abuse initiation. The model is then fitted to data on methamphetamine users less than 20 years old reporting methamphetamine as their primary substance of abuse in the treatment centres of Cape Town and parameter values that give the best fit are chosen. Results show that the proportion of methamphetamine users less than 20 years old reporting methamphetamine as their primary substance of abuse will continue to decrease in Cape Town of South Africa. The results suggest that intervention programs targeted at reducing adolescence methamphetamine abuse, are positively impacting methamphetamine abuse.

The role of mobility and health disparities on the transmission dynamics of Tuberculosis

Background

The transmission dynamics of Tuberculosis (TB) involve complex epidemiological and socio-economical interactions between individuals living in highly distinct regional conditions. The level of exogenous reinfection and first time infection rates within high-incidence settings may influence the impact of control programs on TB prevalence. The impact that effective population size and the distribution of individuals’ residence times in different patches have on TB transmission and control are studied using selected scenarios where risk is defined by the estimated or perceive first time infection and/or exogenous re-infection rates.

Methods

This study aims at enhancing the understanding of TB dynamics, within simplified, two patch, risk-defined environments, in the presence of short term mobility and variations in reinfection and infection rates via a mathematical model. The modeling framework captures the role of individuals’ ‘daily’ dynamics within and between places of residency, work or business via the average proportion of time spent in residence and as visitors to TB-risk environments (patches). As a result, the effective population size of Patch i (home of i-residents) at time t must account for visitors and residents of Patch i, at time t.

Results

The study identifies critical social behaviors mechanisms that can facilitate or eliminate TB infection in vulnerable populations. The results suggest that short-term mobility between heterogeneous patches contributes to significant overall increases in TB prevalence when risk is considered only in terms of direct new infection transmission, compared to the effect of exogenous reinfection. Although, the role of exogenous reinfection increases the risk that come from large movement of individuals, due to catastrophes or conflict, to TB-free areas.

Conclusions

The study highlights that allowing infected individuals to move from high to low TB prevalence areas (for example via the sharing of treatment and isolation facilities) may lead to a reduction in the total TB prevalence in the overall population. The higher the population size heterogeneity between distinct risk patches, the larger the benefit (low overall prevalence) under the same “traveling” patterns. Policies need to account for population specific factors (such as risks that are inherent with high levels of migration, local and regional mobility patterns, and first time infection rates) in order to be long lasting, effective and results in low number of drug resistant cases.

Why do students quit school? Implications from a dynamical modelling study

In 2012, more than three million students dropped out from high school. At this pace, we will have more than 30 million Americans without a high school degree by 2022 and relatively high dropout rates among Hispanic and African American students. We have developed and analysed a data-driven mathematical model that includes multiple interacting mechanisms and estimates of parameters using data from a specifically designed survey applied to a certain group of students of a high school in Chicago to understand the dynamics of dropouts. Our analysis suggests students' academic achievement is directly related to the level of parental involvement more than any other factors in our study. However, if the negative peer influence (leading to lower academic grades) increases beyond a critical value, the effect of parental involvement on the dynamics of dropouts becomes negligible.

Modelling Drug Abuse Epidemics in the Presence of Limited Rehabilitation Capacity

The abuse of drugs is now an epidemic globally whose control has been mainly through rehabilitation. The demand for drug abuse rehabilitation has not been matched with the available capacity resulting in limited placement of addicts into rehabilitation. In this paper, we model limited rehabilitation through the Hill function incorporated into a system of nonlinear ordinary differential equations. Not every member of the community is equally likely to embark on drug use, risk structure is included to help differentiate those more likely (high risk) to abuse drugs and those less likely (low risk) to abuse drugs. It is shown that the model has multiple equilibria, and using the centre manifold theory, the model exhibits the phenomenon of backward bifurcation whose implications to rehabilitation are discussed. Sensitivity analysis and numerical simulations are performed. The results show that saturation in rehabilitation will in the long run lead to the escalation of drug abuse. This means that limited access to rehabilitation has negative implications in the fight against drug abuse where rehabilitation is the main form of control. This suggests that increased access to rehabilitation is likely to lower the drug abuse epidemic.

Complex dynamics in an alcoholism model with the impact of Twitter

A novel alcoholism model which involves impact of Twitter is formulated. It is shown that the model has multiple equilibria. Stability of all the equilibria are obtained in terms of the basic reproductive number R₀. Using the center manifold theory, the occurrence of backward and forward bifurcation for a certain defined range of R₀ are established. Furthermore, the existence of Hopf bifurcation is also established by regarding the transmission coefficient β as the bifurcation parameter. Numerical simulations and sensitivity analysis on a few parameters are also carried out. Our results show that Twitter can serve as a good indicator of alcoholism model and affect the spread of the drinking.

Impact of media coverage on the drinking dynamics in the scale-free network

A binge drinking model with the impact of media in the scale-free network is proposed. The basic reproduction number [Formula: see text] is derived by the next generation matrix method. Stability of the alcohol free equilibrium is proved by the comparison theorem. Existence and uniqueness of the alcohol present equilibrium is also obtained. Furthermore, the permanence of the system and the influence of media coverage on the drinking dynamics are studied, and the difference between our model on heterogeneous and homogeneous networks is also discussed. Numerical simulations are presented to illustrate our theoretical results. Our results show that media coverage does not change the value of [Formula: see text] but it is an effective measure in reducing alcohol problems.

Modelling effects of public health educational campaigns on drinking dynamics

This paper deals with the global property of a drinking model with public health educational campaigns. With the help of Lyapunov function, global stability of equilibria of the model is derived. The alcohol-free equilibrium is globally asymptotically stable and the alcohol problems are eliminated from population if [Formula: see text]. A unique alcohol present equilibrium is globally asymptotically stable if [Formula: see text]. Furthermore, the basic reproductive [Formula: see text] for the model is compared with the basic reproductive number [Formula: see text] for the absence of public health educational campaigns. We conclude that the public health educational campaigns of drinking individuals can slow down the drinking dynamics. Some numerical simulations are also given to explain our conclusions.

Sociological phenomena as multiple nonlinearities: MTBI's new metaphor for complex human interactions

Mathematical models are well-established as metaphors for biological and epidemiological systems. The framework of epidemic modeling has also been applied to sociological phenomena driven by peer pressure, notably in two dozen dynamical systems research projects developed through the Mathematical and Theoretical Biology Institute, and popularized by authors such as Gladwell (2000). This article reviews these studies and their common structures, and identifies a new mathematical metaphor which uses multiple nonlinearities to describe the multiple thresholds governing the persistence of hierarchical phenomena, including the situation termed a "backward bifurcation'' in mathematical epidemiology, where established phenomena can persist in circumstances under which the phenomena could not initially emerge.

From the guest editors

Carlos Castilo-Chavez is a Regents Professor, a Joaquin Bustoz Jr. Professor of Mathematical Biology, and a Distinguished Sustainability Scientist at Arizona State University. His research program is at the interface of the mathematical and natural and social sciences with emphasis on (i) the role of dynamic social landscapes on disease dispersal; (ii) the role of environmental and social structures on the dynamics of addiction and disease evolution, and (iii) Dynamics of complex systems at the interphase of ecology, epidemiology and the social sciences. Castillo-Chavez has co-authored over two hundred publications (see goggle scholar citations) that include journal articles and edited research volumes. Specifically, he co-authored a textbook in Mathematical Biology in 2001 (second edition in 2012); a volume (with Harvey Thomas Banks) on the use of mathematical models in homeland security published in SIAM's Frontiers in Applied Mathematics Series (2003); and co-edited volumes in the Series Contemporary Mathematics entitled '' Mathematical Studies on Human Disease Dynamics: Emerging Paradigms and Challenges'' (American Mathematical Society, 2006) and Mathematical and Statistical Estimation Approaches in Epidemiology (Springer-Verlag, 2009) highlighting his interests in the applications of mathematics in emerging and re-emerging diseases. Castillo-Chavez is a member of the Santa Fe Institute's external faculty, adjunct professor at Cornell University, and contributor, as a member of the Steering Committee of the '' Committee for the Review of the Evaluation Data on the Effectiveness of NSF-Supported and Commercially Generated Mathematics Curriculum Materials,'' to a 2004 NRC report. The CBMS workshop '' Mathematical Epidemiology with Applications'' lectures delivered by C. Castillo-Chavez and F. Brauer in 2011 have been published by SIAM in 2013.

The mathematical and theoretical biology institute--a model of mentorship through research

This article details the history, logistical operations, and design philosophy of the Mathematical and Theoretical Biology Institute (MTBI), a nationally recognized research program with an 18-year history of mentoring researchers at every level from high school through university faculty, increasing the number of researchers from historically underrepresented minorities, and motivating them to pursue research careers by allowing them to work on problems of interest to them and supporting them in this endeavor. This mosaic profile highlights how MTBI provides a replicable multi-level model for research mentorship.

Influence of environmental factors on college alcohol drinking patterns

Alcohol abuse is a major problem, especially among students on and around college campuses. We use the mathematical framework of [16] and study the role of environmental factors on the long term dynamics of an alcohol drinking population. Sensitivity and uncertainty analyses are carried out on the relevant functions (for example, on the drinking reproduction number and the extinction time of moderate and heavy drinking because of interventions) to understand the impact of environmental interventions on the distributions of drinkers. The reproduction number helps determine whether or not the high-risk alcohol drinking behavior will spread and become persistent in the population, whereas extinction time of high-risk drinking measures the effectiveness of control programs. We found that the reproduction number is most sensitive to social interactions, while the time to extinction of high-risk drinkers is significantly sensitive to the intervention programs that reduce initiation, and the college drop-out rate. The results also suggest that in a population, higher rates of intervention programs in low-risk environments (more than intervention rates in high-risk environments) are needed to reduce heavy drinking in the population.

An SIS model for cultural trait transmission with conformity bias

Epidemiological models have been applied to human health-related behaviors that are affected by social interaction. Typically these models have not considered conformity bias, that is, the exaggerated propensity to adopt commonly observed behaviors or opinions, or content biases, where the content of the learned trait affects the probability of adoption. Here we consider an interaction of these two effects, presenting an SIS-type model for the spread and persistence of a behavior which is transmitted via social learning. Uptake is controlled by a nonlinear dependence on the proportion of individuals demonstrating the behavior in a population. Three equilibrium solutions are found, their linear stability is analyzed and the results are compared with a model for unbiased social learning. Our analysis focuses on the effects of the strength of conformity bias and the effects of content biases which alter a conformity threshold frequency of the behavior, above which there is an exaggerated propensity for adoption. The strength of the conformity bias is found to qualitatively alter the predictions regarding whether the trait becomes endemic within the population and the proportion of individuals who display the trait when it is endemic. As the conformity strength increases, the number of feasible equilibrium solutions increases from two to three, leading to a situation where the stable equilibrium attained is dependent upon the initial state. Varying the conformity threshold frequency directionally alters the behavior invasion threshold. Finally we discuss the possible application of this model to binge drinking behavior.

MODELING BINGE DRINKING

We develop a two-stage (four component) model for youths with serious drinking problems and their treatment. The youths with alcohol problems are split into two classes, namely those who admit to having a problem and those who do not. It is shown that the model possesses two steady states, one where people have no alcohol problems and one where there is an endemic state involving those with an alcohol problem. The stability of these states is analyzed and a threshold established such that each state will be stable depending on whether the incidence rate is above or below the threshold. The model is analyzed in the context of actual data.

Heaviest drinking locations and the most drunk there predict the likelihood of fighting and being assaulted: Results from the 2000 US National Alcohol Survey

Preference for on-premise drinking affects likelihood of aggression but how venue affects victimization by other drinkers is less studied. We investigated influence of heavy consumption in specific venues on fighting and assaults by other drinkers in the 2000 US National Alcohol Surveys, a representative telephone survey of adults (n = 7,612). In the prior year 4.5% current drinkers were assaulted by drinkers, while < 2% reported fighting while drinking. Logistic regression analyses showed that where one drank most, and usual and peak amounts drunk there each influenced risks of fighting and (less) being assaulted. For drinking and fighting, heaviest context, usual amount, and difference between usual and peak were all highly significant but adding age and impulsivity/sensation seeking eliminated effect of venue. Victimization risk curves for maximum were exponential: a peak of 10+ drinks showed odds ratios when at another's home, one's own home, and a bar of 4.5, 5.3 and 10.3, respectively (reference 1-2 home drinks); risk curves were steeper for fighting. Maximum amount consumed dominates the venue in which one drinks the most, once selectivity based on personal characteristics is attended to. We suggest interventions should emphasize ways of addressing overdrinking within a range of settings.

Types of drinkers and drinking settings: an application of a mathematical model

AIMS

US college drinking data and a simple population model of alcohol consumption are used to explore the impact of social and contextual parameters on the distribution of light, moderate and heavy drinkers. Light drinkers become moderate drinkers under social influence, moderate drinkers may change environments and become heavy drinkers. We estimate the drinking reproduction number, R(d) , the average number of individual transitions from light to moderate drinking that result from the introduction of a moderate drinker in a population of light drinkers.

DESIGN AND SETTINGS

Ways of assessing and ranking progression of drinking risks and data-driven definitions of high- and low-risk drinking environments are introduced. Uncertainty and sensitivity analyses, via a novel statistical approach, are conducted to assess R(d) variability and to analyze the role of context on drinking dynamics.

FINDINGS

Our estimates show R(d) well above the critical value of 1. R(d) estimates correlate positively with the proportion of time spent by moderate drinkers in high-risk drinking environments. R(d) is most sensitive to variations in local social mixing contact rates within low-risk environments. The parameterized model with college data suggests that high residence times of moderate drinkers in low-risk environments maintain heavy drinking.

CONCLUSIONS

With regard to alcohol consumption in US college students, drinking places, the connectivity (traffic) between drinking venues and the strength of socialization in local environments are important determinants in transitions between light, moderate and heavy drinking as well as in long-term prediction of the drinking dynamics.