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犯罪与吸毒共动力学的数学建模与分析。

Mathematical modeling and analysis of the co-dynamics of crime and drug abuse.

机构信息

Department of Mathematics, Debre Berhan University, 445, Debre Berhan, Ethiopia.

Pan African University Institute for Basic Sciences, Technology and Innovation (PAUSTI), Nairobi, Kenya.

出版信息

Sci Rep. 2024 Nov 2;14(1):26461. doi: 10.1038/s41598-024-75034-8.

DOI:10.1038/s41598-024-75034-8
PMID:39488534
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11531553/
Abstract

This study explores the dynamics of crime and substance abuse within a population by developing a novel mathematical model that integrates social interactions, rehabilitation efforts, and relapse probabilities. The model introduces a critical metric, the control reproduction number [Formula: see text], to quantify the invasion threshold for these behaviors. The findings reveal that the crime/substance-free equilibrium is globally asymptotically stable when [Formula: see text]. At the same time, entrenched equilibria become stable where [Formula: see text]. Additionally, the model predicts the potential for a co-existent equilibrium where crime/substance abuse and a free state can coexist if all reproduction numbers exceed unity. Sensitivity analysis identifies key factors influencing [Formula: see text], including behavioral transmission, internal progression rates, intervention efficacy, and recovery/relapse probabilities. Numerical simulations validate theoretical predictions regarding the stability of different equilibria, highlighting the critical importance of interventions targeting transmission reduction and rehabilitation efficiency. The research underscores the significance of understanding invasion dynamics for the coexistence of behaviors. It demonstrates the utility of mathematical modeling in elucidating the spread of social phenomena and informing effective control strategies.

摘要

本研究通过开发一种新的数学模型，将社会互动、康复努力和复发概率整合在一起，探索了人群中犯罪和药物滥用的动态。该模型引入了一个关键指标，控制繁殖数 [Formula: see text]，以量化这些行为的入侵阈值。研究结果表明，当 [Formula: see text] 时，无犯罪/无药物滥用的平衡点是全局渐近稳定的。同时，如果所有繁殖数都超过 1，则固有的平衡点也变得稳定。此外，该模型预测了如果所有繁殖数都超过 1，则犯罪/药物滥用和自由状态可以共存的共存平衡点的可能性。敏感性分析确定了影响 [Formula: see text] 的关键因素，包括行为传播、内部进展率、干预效果和恢复/复发概率。数值模拟验证了关于不同平衡点稳定性的理论预测，突出了针对传播减少和康复效率的干预的重要性。该研究强调了理解行为共存的入侵动态的重要性。它展示了数学建模在阐明社会现象传播和为有效控制策略提供信息方面的效用。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4964/11531553/a6477fd1b14d/41598_2024_75034_Fig9_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4964/11531553/ab8646290a06/41598_2024_75034_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4964/11531553/a6477fd1b14d/41598_2024_75034_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4964/11531553/e9416437356c/41598_2024_75034_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4964/11531553/403d01dba818/41598_2024_75034_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4964/11531553/59077b538a67/41598_2024_75034_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4964/11531553/d632c4149402/41598_2024_75034_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4964/11531553/a516f2ef84f6/41598_2024_75034_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4964/11531553/bea666a18101/41598_2024_75034_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4964/11531553/823603e7e4c5/41598_2024_75034_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4964/11531553/ab8646290a06/41598_2024_75034_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4964/11531553/a6477fd1b14d/41598_2024_75034_Fig9_HTML.jpg

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