On the Role of Imitation on Adolescence Methamphetamine Abuse Dynamics

A Risk-Structured Model of the Influence of Mental Health on Opioid Addiction

In 2021, over 80,000 of the 107,622 overdose deaths in the United States involved opioids, with opioid use disorder (OUD) and fatal overdoses imposing economic costs exceeding $1 trillion in 2017. Mathematical modeling provides an important tool for understanding the dynamics of the opioid epidemic and evaluating the potential benefits of different treatment and prevention strategies. In particular, we extend the Susceptible-Infected-Recovered paradigm for modeling infectious diseases to the opioid crisis. While existing compartmental models of OUD often assume equal risk of addiction across individuals, this assumption overlooks the significant role of risk heterogeneity. Unlike previous models that assume uniform addiction risk, our model incorporates risk stratification to account for the disproportionate burden among individuals with mental health disorders, who represent 20% of the U.S. population but account for over half of opioid prescriptions and misuse. Our compartmental model distinguishes between addiction pathways initiated by prescription opioids and those driven by social influences. Using existing data, we calibrate the model to estimate key parameters and quantify the impact of risk heterogeneity, offering insights to the addiction process.

Social Pressure from a Core Group can Cause Self-Sustained Oscillations in an Epidemic Model

Let the individuals of a population be divided into two groups with different personal habits. The core group is associated with health risk behaviors; the non-core group avoids unhealthy activities. Assume that the infected individuals of the core group can spread a contagious disease to the whole population. Also, assume that cure does not confer immunity. Here, an epidemiological model written as a set of ordinary differential equations is proposed to investigate the infection propagation in this population. In the model, migrations between these two groups are allowed; however, the transitions from the non-core group into the core group prevail. These migrations can be either spontaneous or stimulated by social pressure. It is analytically shown that, in the scenario of spontaneous migration, the disease is either naturally eradicated or chronically persists at a constant level. In the scenario of stimulated migration, in addition to eradication and constant persistence, self-sustained oscillations in the number of sick individuals can also be found. These analytical results are illustrated by numerical simulations and discussed from a public health perspective.

A Scoping Review of Drug Epidemic Models

The phenomenon of drug epidemics has been a global issue in the past decades, causing enormous damages to the physical and mental health of drug users and social well-being. Despite great efforts to curb drug epidemics at the governmental or social level, the total number of drug users has still been on the rise in recent years, along with illicit production and trafficking around the world. Inspired by dynamical epidemic models of infectious disease, a flourishment of promising results has been observed in the exploration of drug epidemic models. In this review, we aim to provide a scoping review of all existing drug epidemic modeling studies, and it has been shown that most studies focused on analyses of theoretical behaviors of the model systems, lacking emphasis on practical applications in real settings. We found that the drug epidemic models were characterized by a longer time scale, no incubation period, no significant prevention vaccines interfered, and population specificity. This review could assist policymakers and public health workers in gaining deeper insights into modeling tools, and help modelers improve their works, thus narrowing gaps between mathematical epidemiology and public health studies.

Modeling the Dynamics of Drug Spreading in China

Drug abuse remains one of the major public health issues at the global level. In this article, we propose a drug epidemic model with a complete addiction-rehabilitation-recovery process, which allows the initiation of new users under the influence of drug addicts undergoing treatment and hidden drug addicts. We first conduct qualitative analyses of the dynamical behaviors of the model, including the existence and positivity of the solutions, the basic reproduction number, global asymptotic stabilities of both the drug-free and the drug-persistent equilibria, as well as sensitivity analysis. Then we use the model to predict the drug epidemic in China during 2020-2030. Finally, we numerically simulate the potential impact of intervention strategies on different drug users. The results show that the drug epidemic will decrease significantly during 2020-2030, and the most effective intervention strategy to eliminate drug epidemics is to strengthen the investigation and rehabilitation admission of hidden drug users.

Modelling the role of correctional services on gangs: insights through a mathematical model

Research has shown that gang membership increases the chances of offending, antisocial behaviour and drug use. Gang membership should be acknowledged as part of crime prevention and policy designs, and when developing interventions and preventative programmes. Correctional services are designed to rehabilitate convicted offenders. We formulate a deterministic mathematical model using nonlinear ordinary differential equations to investigate the role of correctional services on the dynamics of gangs. The recruitment into gang membership is assumed to happen through an imitation process. An epidemic threshold value, [Formula: see text], termed the gang reproduction number, is proposed and defined herein in the gangs' context. The model is shown to exhibit the phenomenon of backward bifurcation. This means that gangs 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 gang initiation. The critical efficacy ε* is evaluated and the implications of having functional correctional services are discussed.