Threshold dynamics of a delayed multi-group heroin epidemic model in heterogeneous populations

Liu, Lili; Liu, Xianning; Wang, Jinliang

doi:10.3934/dcdsb.2016064

Cited by 11 publications

(5 citation statements)

References 27 publications

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“…In addition to obtaining threshold dynamics of the system, the authors have shown the persistence of the heroin epidemic for sufficiently large networks. Another delayed multi-group heroin epidemic model in the heterogeneous population was considered by Liu et al in 2016, where distributed delay was adopted for both initiates and relapse rates [ 35 ]. The authors finished proofs of the threshold dynamics through the graph-theoretic approach and Krichhoff’s matrix tree theorem and performed simulation studies for the case of two groups.…”

Section: Resultsmentioning

confidence: 99%

A Scoping Review of Drug Epidemic Models

Wang

Tang

et al. 2022

IJERPH

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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.

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Section: Resultsmentioning

confidence: 99%

A Scoping Review of Drug Epidemic Models

Wang

Tang

et al. 2022

IJERPH

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“…Secondly, the scarcity of historical data occurred due to former scopes of statistics adopted by the NNCC, which only provided accumulative numbers of drug users, and there was no other direct source available to secure the data of interest. Drug-use patterns and demographic characteristics may differ greatly among different subgroups divided according to age, gender, drug type consumed, etc., which requires advanced mathematical tools such as stratified models or partial differential equations [ 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 ]. Despite these limitations, our model still offers a universally applicable tool for prediction and analysis of the drug situation, and the complex issues listed above will be considered in our future research.…”

Section: Discussionmentioning

confidence: 99%

“…Other modification studies, which were mostly heroin epidemic models, took advantage of various mathematical tools to account for practical factors. For example, delayed differential equations were used to simulate processes with known durations [ 20 , 21 , 22 , 23 ], partial differential equations were utilized to incorporate the effect of age or treatment duration [ 24 , 25 , 26 , 27 , 28 , 29 ], multi-layered models were proposed when population heterogeneity was involved [ 30 , 31 , 32 , 33 ], and stochastic differential equations were formulated to reflect unexpected fluctuations in reality [ 34 , 35 , 36 , 37 , 38 ]. In addition to theoretical analyses, some synthetic drug epidemic models were applied to real settings and fitted to historical data, most of which were based on methamphetamine epidemics in South Africa [ 39 , 40 , 41 , 42 , 43 , 44 ].…”

Section: Introductionmentioning

confidence: 99%

Modeling the Dynamics of Drug Spreading in China

Tang

Yan

et al. 2021

IJERPH

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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.

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“…In [19], Liu and Zhang studied the global behavior of a heroin epidemic model with distributed time delay: the drug-free equilibrium is globally asymptotically stable if the basic reproduction number R 0 is less than 1, whereas a disease endemic equilibrium is locally asymptotically stable and the system is uniformly persistent if R 0 > 1. For other studies on the drug epidemic models with time delay, see, e.g., [9,13,20,21].…”

mentioning

confidence: 99%

Mathematical analysis of an age structured heroin-cocaine epidemic model

Chekroun¹,

Frioui²,

Kuniya³

et al. 2020

DCDS-B

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This paper is devoted to studying the dynamics of a certain age structured heroin-cocaine epidemic model. More precisely, this model takes into account the following unknown variables: susceptible individuals, heroin users, cocaine users and recovered individuals. Each one of these classes can change or interact with others. In this paper, firstly, we give some results on the existence, uniqueness and positivity of solutions. Next, we obtain a threshold value r(Ψ [0]) such that an endemic equilibrium exists if r(Ψ [0]) > 1. We then show that if r(Ψ [0]) < 1, then the disease-free equilibrium is globally asymptotically stable, whereas if r(Ψ [0]) > 1, then the system is uniformly persistent. Moreover, for r(Ψ [0]) > 1, we show that the endemic equilibrium is globally asymptotically stable under an additional assumption that epidemic parameters for heroin users and cocaine users are same. Finally, some numerical simulations are presented to illustrate our theoretical results.

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Threshold dynamics of a delayed multi-group heroin epidemic model in heterogeneous populations

Cited by 11 publications

References 27 publications

A Scoping Review of Drug Epidemic Models

A Scoping Review of Drug Epidemic Models

Modeling the Dynamics of Drug Spreading in China

Mathematical analysis of an age structured heroin-cocaine epidemic model

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