Impact of combined effects of vectors, protective measures, and vaccination under threshold policy control on the SISV model.

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2025-05-01 DOI:10.1063/5.0256966
Xiong Zhang, Zhongyi Xiang
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引用次数: 0

Abstract

This paper introduces a novel class of Filippov susceptible-infected-susceptible-vaccinated model that considers the combined effects of media coverage, protective measures, and vaccination. Unlike traditional models that focus on a single control measure, this study reveals more intricate dynamic behaviors arising from the synergistic impact of these three strategies. We use the scale of infected individuals and their rate of change as criteria for implementing control measures, conducting a comprehensive evaluation. By utilizing the characteristics of the Lambert W function, we effectively convert these criteria into a threshold value linked to the susceptible population, thereby facilitating the analysis of the dynamic behaviors of the two subsystems. Utilizing the theoretical framework of Filippov systems, we derive the conditions for the existence of sliding segments, sliding dynamics, various types of equilibria, and the occurrence of sliding bifurcations. Through qualitative analysis, and based on the critical thresholds R0i(i=1,2), we elucidate the complex dynamics of the proposed model, including scenarios of monostable, bistable, or even tristable coexistence. Numerical simulations further explore the effects of key parameters related to the treatment strategies, demonstrating that media coverage, protective measures, and vaccination play pivotal roles in controlling the spread of the disease. Our findings indicate that by selecting appropriate threshold values, it is possible to effectively limit the peak number of infected individuals and the overall scale of the outbreak to a desired level. This provides a robust control strategy for managing emergent infectious diseases that cannot be immediately eradicated.

阈值政策控制下媒介、保护措施和疫苗接种的联合效应对SISV模型的影响。
本文介绍了一类新的菲利波夫易感-感染-易感-接种模型,该模型考虑了媒介覆盖、保护措施和疫苗接种的综合效应。与关注单一控制措施的传统模型不同,本研究揭示了这三种策略的协同影响所产生的更复杂的动态行为。我们以受感染个体的规模及其变化率作为实施控制措施的标准,进行全面评估。利用Lambert W函数的特性,将这些准则有效地转化为与易感人群相关联的阈值,从而便于对两个子系统的动态行为进行分析。利用Filippov系统的理论框架,我们推导了滑动段存在的条件、滑动动力学、各种类型的平衡以及滑动分岔的发生。通过定性分析,基于临界阈值R0i(i=1,2),我们阐明了所提出模型的复杂动力学,包括单稳态、双稳态甚至三稳态共存的场景。数值模拟进一步探讨了与治疗策略相关的关键参数的影响,表明媒体报道、防护措施和疫苗接种在控制疾病传播方面发挥了关键作用。我们的研究结果表明,通过选择适当的阈值,可以有效地将感染个体的高峰人数和爆发的总体规模限制在理想的水平。这为管理不能立即根除的突发传染病提供了强有力的控制战略。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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