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

Parametric analysis of SARS-CoV-2 dose-response models in transportation scenarios

Transportation systems involve high-density crowds of geographically diverse people with variations in susceptibility; therefore, they play a large role in the spread of infectious diseases like SARS-CoV-2. Dose-response models are widely used to model the relationship between the trigger of a disease and the level of exposure in transmission scenarios. In this study, we quantified and bounded viral exposure-related parameters using empirical data from five transportation-related events of SARS-CoV-2 transmission. Dose-response models were then applied to parametrically analyze the infection spread in generic transportation systems, including a single-aisle airplane, bus, and railway coach, and then examined the mitigating efficiency of masks by performing a sensitivity analysis of the related factors. We found that dose level significantly affected the number of secondary infections. In general, we observed that mask usage reduced infection rates at all dose levels and that high-quality masks equivalent to FFP2/N95 masks are effective for all dose levels. In comparison, we found that lower-quality masks exhibit limited mitigation efficiency, especially in the presence of high dosage. The sensitivity analysis indicated that a reduction in the infection distance threshold is a critical factor in mask usage.

Structural instability and linear allocation control in generalized models of substance use disorder

Substance use disorder (SUD) is a complex disease involving nontrivial biological, psychological, environmental, and social factors. While many mathematical studies have proposed compartmental models for SUD, almost all of these exclusively model new cases as the result of an infectious process, neglecting any SUD that was primarily developed in social isolation. While these decisions were likely made to facilitate mathematical analysis, isolated SUD development is critical for the most common substances of abuse today, including opioid use disorder developed through prescription use and alcoholism developed primarily due to genetic factors or stress, depression, and other psychological factors. In this paper we will demonstrate that even a simple infectious disease model is structurally unstable with respect to a linear perturbation in the infection term - precisely the sort of term necessary to model SUD development in isolation. This implies that models of SUD which exclusively treat problematic substance use as an infectious disease will have misleading dynamics whenever a non-trivial rate of isolated SUD development exists in actuality. As we will show, linearly perturbed SUD models do not have a use disorder-free equilibrium. To investigate management strategies, we implement optimal control techniques with the goal of minimizing the number of SUD cases over time.

Alcohol consumption as a socially contagious phenomenon in the Framingham Heart Study social network

We use longitudinal social network data from the Framingham Heart Study to examine the extent to which alcohol consumption is influenced by the network structure. We assess the spread of alcohol use in a three-state SIS-type model, classifying individuals as abstainers, moderate drinkers, and heavy drinkers. We find that the use of three-states improves on the more canonical two-state classification, as the data show that all three states are highly stable and have different social dynamics. We show that when modelling the spread of alcohol use, it is important to model the topology of social interactions by incorporating the network structure. The population is not homogeneously mixed, and clustering is high with abstainers and heavy drinkers. We find that both abstainers and heavy drinkers have a strong influence on their social environment; for every heavy drinker and abstainer connection, the probability of a moderate drinker adopting their drinking behaviour increases by [Formula: see text] and [Formula: see text], respectively. We also find that abstinent connections have a significant positive effect on heavy drinkers quitting drinking. Using simulations, we find that while both are effective, increasing the influence of abstainers appears to be the more effective intervention compared to reducing the influence of heavy drinkers.

A mathematical model with nonlinear relapse: conditions for a forward-backward bifurcation

We constructed a Susceptible-Addicted-Reformed model and explored the dynamics of nonlinear relapse in the Reformed population. The transition from susceptible considered at-risk is modeled using a strictly decreasing general function, mimicking an influential factor that reduces the flow into the addicted class. The basic reproductive number is computed, which determines the local asymptotically stability of the addicted-free equilibrium. Conditions for a forward-backward bifurcation were established using the basic reproductive number and other threshold quantities. A stochastic version of the model is presented, and some numerical examples are shown. Results showed that the influence of the temporarily reformed individuals is highly sensitive to the initial addicted population.

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.

"On a night like this": A mixed-methods approach to understanding high-risk drinking events in college students

BACKGROUND

Previous research indicates college students report heavier drinking on certain events (e.g., 21st birthday). While past research has identified heavier drinking events, students' own reports of which events are associated with elevated drinking remains understudied. The current study utilized mixed methods to explore potential high-risk drinking events (HRDE) for college student drinkers and how these events differed from typical drinking and each other.

METHODS

College student drinkers (N = 204) reported the number of drinks they consume on nine predetermined events (e.g., Halloween). Students also responded to open-ended questions listing five events during which they had elevated drinking and indicating the amount consumed on each event. Open-ended responses were coded into similar event categories. Descriptive statistics for drinks consumed were calculated for predetermined and coded open-ended events. Chi-square analyses assessed differences in endorsement of open-ended events by birth sex, age group, and Greek membership. Two multilevel count regressions assessed within-person differences in number of drinks consumed between participants' typical drinking occasions and (1) highly endorsed open-ended events and (2) predetermined events.

RESULTS

For all open-ended event categories, average number of drinks consumed exceeded heavy episodic drinking thresholds; however, there was substantial variability. Comparing predetermined events to participants' typical drinking indicated elevated drinking on participants' birthdays, New Year's Eve, Halloween, Finals, and Spring Break; significant differences between events also emerged. Comparison of open-ended categories to participants' typical drinking indicated elevated drinking on birthdays, celebrations, parties, and holidays; however, there were no significant differences between open-ended events.

CONCLUSIONS

Students who drink alcohol report heavier drinking on specific calendar-based events (e.g., Spring Break). However, students also report non-calendar-related events (e.g., non-specific parties) as some of their highest drinking events. More research is needed to understand how intervention and prevention programs can be adapted to target both known calendar-based HRDE, and unknown, idiosyncratic HRDE.

Identifying mitigation strategies for COVID-19 superspreading on flights using models that account for passenger movement

Background

Despite commercial airlines mandating masks, there have been multiple documented events of COVID-19 superspreading on flights. Conventional models do not adequately explain superspreading patterns on flights, with infection spread wider than expected from proximity based on passenger seating. An important reason for this is that models typically do not consider the movement of passengers during the flight, boarding, or deplaning. Understanding the risks for each of these aspects could provide insight into effective mitigation measures.

Methods

We modeled infection risk from seating and fine-grained movement patterns – boarding, deplaning, and inflight movement. We estimated infection model parameters from a prior superspreading event. We validated the model and the impact of interventions using available data from three flights, including cabin layout and seat locations of infected and uninfected passengers, to suggest interventions to mitigate COVID-19 superspreading events during air travel. Specifically, we studied: 1) London to Hanoi with 201 passengers, including 13 secondary infections among passengers; 2) Singapore to Hangzhou with 321 passengers, including 12 to 14 secondary infections; 3) a non-superspreading event on a private jet in Japan with 9 passengers and no secondary infections.

Results

Our results show that the inclusion of passenger movement better explains the infection spread patterns than conventional models do. We also found that FFP2/N95 mask usage would have reduced infection by 95–100%, while cloth masks would have reduced it by only 40–80%. Results indicate that leaving the middle seat vacant is effective in reducing infection, and the effectiveness increases when combined with good quality masks. However, with a good mask, the risk is quite low even without the middle seats being empty.

Conclusions

Our results suggest the need for more stringent guidelines to reduce aviation-related superspreading events of COVID-19.

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.

Analytical Estimation of Data-Motivated Time-Dependent Disease Transmission Rate: An Application to Ebola and Selected Public Health Problems

Obtaining reasonable estimates for transmission rates from observed data is a challenge when using mathematical models to study the dynamics of ?infectious? diseases, like Ebola. Most models assume the transmission rate of a contagion either does not vary over time or change in a fixed pre-determined adhoc ways. However, these rates do vary during an outbreak due to multitude of factors such as environmental conditions, social behaviors, and public-health interventions deployed to control the disease, which are in-part guided by changing size of an outbreak. We derive analytical estimates of time-dependent transmission rate for an epidemic in terms of either incidence or prevalence using a standard mathematical SIR-type epidemic model. We illustrate applicability of our method by applying data on various public health problems, including infectious diseases (Ebola, SARS, and Leishmaniasis) and social issues (obesity and alcohol drinking) to compute transmission rates over time. We show that time-dependent transmission rate estimates can have a large variation, depending on the type of available data and other epidemiological parameters. Time-dependent estimation of transmission rates captures the dynamics of the problem better and can be utilized to understand disease progression more accurately.

Alcohol Mixed with Energy Drinks (AmED) and Negative Alcohol-Related Consequences among South Korean College Students

Consumption of alcohol mixed with energy drinks (AmED) has been associated with various alcohol-related consequences among college students. However, more information is required to assess how this relationship is affected by sociodemographic and environmental factors. This paper investigates the association between AmED consumption and negative alcohol-related consequences while (1) stratifying AmED users by sex, (2) examining a range of outcomes specific to the college context (e.g., missing class), and (3) controlling for drinking frequency and amount. We surveyed and analyzed the data of 4592 students in a nationally representative sample of 82 colleges in South Korea. Multiple linear regression analysis was used to identify the association between AmED use and a number of alcohol-related consequences (ranging from a score of 0–12) while adjusting for covariates, including drinking frequency and intake per drinking session. Of our study population, 22.0% of alcohol-consuming men and 13.4% of alcohol-consuming women reported AmED consumption in the past 12 months. AmED users experienced a greater number of alcohol-related consequences (e.g., missing class, engaging in unplanned sexual activity) than non-AmED users (men β: 0.804, p ≤ 0.0001; women β: 0.522, p ≤ 0.0001). Male AmED users consuming alcohol once a month (β: 1.155, p ≤ 0.0001) and female users consuming less than once a month (β: 1.019, p ≤ 0.0001) experienced the greatest number of consequences compared to non-users, as did AmED users consuming 3–4 drinks per drinking session (men β: 1.012, p ≤ 0.0001; women β: 0.993, p ≤ 0.0001). Our findings reveal that both male and female college students who consume AmED experience a greater number of negative alcohol-related consequences than those who do not. Rather than high-risk drinkers, moderate drinkers who consume alcohol infrequently and/or in low amounts may experience more consequences when consumers of AmED.

Analytical and computational study of an individual-based network model for the spread of heavy drinking

Two simple models for the spread of heavy drinking among a network of individuals are re-introduced and analysed. We provide theorems on the spread of alcohol abuse for these models in cases involving simple connection schemes. Indicators for this spread that resemble the [Formula: see text] used in disease assessment are suggested and studied. We further provide computations with our models on general application networks and begin to study the reliability of the spread indicators.

Trends in alcohol use among young people according to the pattern of consumption on starting university: A 9-year follow-up study

AIM

To identify differences in Risky Consumption (RC) and Binge drinking (BD) trends in students who already followed these patterns of alcohol consumption on starting university and those who did not, and also to try to understand what leads students to engage in these types of behaviour at university.

MATERIAL AND METHODS

Cohort study among university students in Spain (n = 1382). BD and RC were measured with the Alcohol Use Disorders Identification Test at ages 18, 20, 22, 24 and 27 years. Multilevel logistic regression for repeated measures was used to calculate the adjusted Odds Ratios (ORs).

RESULTS

The prevalence rates of RC and BD were lower throughout the study in students who did not follow these patterns of consumption at age 18. For RC and BD, the differences at age 27 years, expressed as percentage points (pp), were respectively 24 pp and 15 pp in women and 29 pp and 25 pp in men. Early age of onset of alcohol use increased the risk of engaging in RC and BD patterns at university, for men (OR = 2.91 & 2.80) and women (OR = 8.14 & 5.53). The same was observed in students living away from the parental home for BD (OR = 3.43 for men & 1.77 for women). Only women were influenced by having positive expectancies for engaging in RC (OR = 1.82) and BD (OR = 1.96).

CONCLUSIONS

The prevalence rates of both RC and BD at age 27 years were much higher among university students who already followed these patterns of consumption at age 18 years, with the differences being proportionally higher among women. Focusing on the age of onset of alcohol consumption and hindering access to alcohol by minors should be priority objectives aimed at preventing students from engaging in these patterns of alcohol consumption at university.

Dynamics of Metabolism and Decision Making During Alcohol Consumption: Modeling and Analysis

Heavy alcohol consumption is considered an important public health issue in the United States as over 88 000 people die every year from alcohol-related causes. Research is being conducted to understand the etiology of alcohol consumption and to develop strategies to decrease high-risk consumption and its consequences, but there are still important gaps in determining the main factors that influence the consumption behaviors throughout the drinking event. There is a need for methodologies that allow us not only to identify such factors but also to have a comprehensive understanding of how they are connected and how they affect the dynamical evolution of a drinking event. In this paper, we use previous empirical findings from laboratory and field studies to build a mathematical model of the blood alcohol concentration dynamics in individuals that are in drinking events. We characterize these dynamics as the result of the interaction between a decision-making system and the metabolic process for alcohol. We provide a model of the metabolic process for arbitrary alcohol intake patterns and a characterization of the mechanisms that drive the decision-making process of a drinker during the drinking event. We use computational simulations and Lyapunov stability theory to analyze the effects of the parameters of the model on the blood alcohol concentration dynamics that are characterized. Also, we propose a methodology to inform the model using data collected in situ and to make estimations that provide additional information to the analysis. We show how this model allows us to analyze and predict previously observed behaviors, to design new approaches for the collection of data that improves the construction of the model, and help with the design of interventions.

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.

Modeling and Analysis of Group Dynamics in Alcohol-Consumption Environments

High-risk drinking is considered a major concern in public health, being the third leading preventable cause of death in the United States. Several studies have been conducted to understand the etiology of high-risk drinking and to design prevention strategies to reduce unhealthy alcohol-consumption and related problems, but there are still major gaps in identifying and investigating the key components that affect the consumption patterns during the drinking event. There is a need to develop tools for the design of methodologies to not only identify such dangerous patterns but also to determine how their dynamics impact the event. In this paper, based on current empirical evidence and observations of drinking events, we model a human group that is in an alcohol-consumption scenario as a dynamical system whose behavior is driven by the interplay between the environment, the network of interactions between the individuals, and their personal motivations and characteristics. We show how this mathematical model complements empirical research in this area by allowing us to analyze, simulate, and predict the drinking group behaviors, to improve the methodologies for field data collection, and to design interventions. Through simulations and Lyapunov stability theory, we provide a computational and mathematical analysis of the impact of the model parameters on the predicted dynamics of the drinking group at the drinking event level. Also, we show how the dynamical model can be informed using data collected in situ and to generate information that can complement the analysis.

Profiles of College Drinkers Defined by Alcohol Behaviors at the Week Level: Replication Across Semesters and Prospective Associations With Hazardous Drinking and Dependence-Related Symptoms

OBJECTIVE

Types of college drinkers have been identified using traditional measures (e.g., 12-month drinking frequency). We used an alternative multidimensional approach based on daily reports of alcohol behaviors to identify college drinker statuses, each with a unique behavioral profile. The current study aimed to (a) identify drinker statuses at the week level across four semesters, (b) examine the predictive utility of drinker status by testing associations with senior-year hazardous drinking and dependence symptoms, and (c) identify concurrent predictors (gender, drinking motivations, hazardous drinking, any dependence symptoms) of senior-year drinker status. We also compared the week-level drinker statuses with drinker statuses identified using traditional measures.

METHOD

A multi-ethnic sample of U.S. college students completed 14-day bursts of daily web surveys across college (91%-96% completed ≥6 daily reports of the sampled week). Analyses focus on nine alcohol-related behaviors (including estimated blood alcohol concentration, pregaming, and drinking games) assessed daily in spring/sophomore year to fall/senior year and drinking motivations, hazardous drinking, and dependence symptoms assessed fall/senior year (n = 569; 56% women).

RESULTS

Four week-level drinker statuses were replicated across semesters: Nondrinker, Light Weekend, Heavy Weekend, and Heavy Frequent. Across semesters, drinker status was associated with senior-year hazardous drinking and any dependence symptoms. Senior-year fun/social motivations were also associated with senior-year drinker status. Differences in behavioral profiles between week-level drinker statuses and those identified using traditional measures were found.

CONCLUSIONS

Replicable week-level drinker statuses were identified, suggesting consistency in possible types of drinking weeks. Drinker statuses were predictive of senior-year hazardous drinking and dependence symptoms.

Reducing HIV Risks in the Places Where People Drink: Prevention Interventions in Alcohol Venues

Apart from individual alcohol drinking behavior, the context or places where people drink play a significant role in HIV transmission risk. In this paper, we review the research that has been conducted on alcohol venues to identify the social and structural factors (e.g., social norms, sexual behavior) that are associated with HIV risk in these places, to review HIV prevention interventions based in alcohol venues, and to discuss appropriate methodologies for alcohol venue research. Alcohol venues are defined here as places that sell or serve alcohol for onsite consumption, including bars, bottle stores, nightclubs, wine shops, and informal shebeens. Despite the many established HIV risk factors at play in alcohol venues, limited prevention strategies have been implemented in such places. A total of 11 HIV prevention interventions or programs were identified. HIV prevention interventions in alcohol venues may be conducted at the individual, social, or structural level. However, multilevel interventions that target more than one level appear to lead to the most sustainable behavior change. Strategies to incorporate alcohol venues in biomedical prevention strategies including antiretroviral therapy for alcohol users are also discussed.

On the Effectiveness of Social Norms Intervention in College Drinking: The Roles of Identity Verification and Peer Influence

BACKGROUND

The application of social norms theory in the study of college drinking centers on the ideas that incorrect perceptions of drinking norms encourage problematic drinking behavior and that correcting misperceptions can mitigate problems. The design and execution of social norms interventions can be improved with a deeper understanding of causal mechanisms connecting misperception to drinking behavior.

METHODS

We develop an agent-based computational simulation that uses identity control theory and peer influence (PI) to model interactions that affect drinking. Using data from the College Alcohol Survey and Social Norms Marketing Research Project, we inform model parameters for agent drinking identities and perceptions. We simulate social norms campaigns that reach progressively larger fractions of the student population, and we consider the strength of the campaign in terms of changing student perception and resulting behavior.

RESULTS

We observe a general reduction in heavy episodic drinking (HED) as students are affected by the intervention. As campaigns reached larger fractions of students, the reduction rate diminishes, in some cases actually making a slight reverse. The way in which students "take the message to heart" can have a significant impact as well: The psychological factors involved in identity control and PI have both positive and negative effects on HED rates. With whom agents associate at drinking events also impacts drinking behavior and intervention effectiveness.

CONCLUSIONS

Simulations suggest that reducing misperception can reduce HED. When agents adhere strongly to identity verification and when misperceptions affect identity appraisals, social norms campaigns can bring about large reductions. PI, self-monitoring, and socializing with like-drinking peers appear to moderate the effect.

Change in neighborhood environments and depressive symptoms in New York City: the Multi-Ethnic Study of Atherosclerosis

Physical and social features of neighborhoods, such as esthetic environments and social cohesion, change over time. The extent to which changes in neighborhood conditions are associated with changes in mental health outcomes has not been well-established. Using data from the MultiEthnic Study of Atherosclerosis, this study investigated the degree to which neighborhood social cohesion, stress, violence, safety and/or the esthetic environment changed between 2002 and 2007 in 103 New York City Census tracts and the associations of these changes with changes in depressive symptoms. Neighborhoods became less stressful, more socially cohesive, safer, and less violent. White, wealthy, highly educated individuals tended to live in neighborhoods with greater decreasing violence and stress and increasing social cohesion. Individuals living in neighborhoods with adverse changes were more likely to have increased CES-D scores, although due to limited sample size associations were imprecisely estimated (P>0.05). Changes in specific features of the neighborhood environment may be associated with changes in level of depressive symptoms among residents.

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.

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.

Mathematical insights in evaluating state dependent effectiveness of HIV prevention interventions

Mathematical models have been used to simulate HIV transmission and to study the use of preexposure prophylaxis (PrEP) for HIV prevention. Often a single intervention outcome over 10 years has been used to evaluate the effectiveness of PrEP interventions. However, different metrics express a wide variation over time and often disagree in their forecast on the success of the intervention. We develop a deterministic mathematical model of HIV transmission and use it to evaluate the public-health impact of oral PrEP interventions. We study PrEP effectiveness with respect to different evaluation methods and analyze its dynamics over time. We compare four traditional indicators, based on cumulative number or fractions of infections prevented, on reduction in HIV prevalence or incidence and propose two additional methods, which estimate the burden of the epidemic to the public-health system. We investigate the short and long term behavior of these indicators and the effects of key parameters on the expected benefits from PrEP use. Our findings suggest that public-health officials considering adopting PrEP in HIV prevention programs can make better informed decisions by employing a set of complementing quantitative metrics.

Regulating availability: how access to alcohol affects drinking and problems in youth and adults

Regulations on the availability of alcohol have been used to moderate alcohol problems in communities throughout the world for thousands of years. In the latter half of the 20th century, quantitative studies of the effects of these regulations on drinking and related problems began in earnest as public health practitioners began to recognize the full extent of the harmful consequences related to drinking. This article briefly outlines the history of this work over four areas, focusing on the minimum legal drinking age, the privatization of alcohol control systems, outlet densities, and hours and days of sale. Some historical background is provided to emphasize the theoretical and empirical roots of this work and to highlight the substantial progress that has been made in each area. In general, this assessment suggests that higher minimum legal drinking ages, greater monopoly controls over alcohol sales, lower outlet numbers and reduced outlet densities, and limited hours and days of sale can effectively reduce alcohol sales, use, and problems. There are, however, substantial gaps in the research literature and a near absence of the quantitative theoretical work needed to direct alcohol-control efforts. Local community responses to alcohol policies are complex and heterogeneous, sometimes reinforcing and sometimes mitigating the effects of availability regulations. Quantitative models of policy effects are essential to accelerate progress toward the formulation and testing of optimal control strategies for the reduction of alcohol problems.

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

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 is 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.