Mathematical modeling of containing the spread of heroin addiction via awareness program

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-10-15 DOI:10.1002/mma.10544

Salih Djilali, Amine Loumi, Soufiane Bentout, Ghilmana Sarmad, Abdessamad Tridane

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Abstract

As many countries are hit by the social economic impact of heroin addiction, there is an urgent need to have an effective awareness program that focuses on educating the population on the danger of heroin addiction and helping the heroin-users quit. This paper aims to study the effect of the awareness program on the spread of heroin dependence using a mathematical model with distributed delay. First, we show the existence threshold parameter $R_{0}$ , which we call the basic reproduction number of the spread of heroin use. We prove, via the Lyapunov direct method, that the drug-free equilibrium is globally asymptotically stable if $R_{0} < 1$ . If $R_{0} > 1$ , the drug dependence persists, and the drug equilibrium is globally asymptotically stable. We give three possible scenarios to find the optimal awareness program strategy that puts the heroin epidemic under control. These scenarios take into consideration the reachability of the population, the immunity against heroin addiction, and the effectiveness of the program to contain the use of heroin in the population and bring $R_{0}$ below one.

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.