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Updated: Sep 10, 2025

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恐惧对空间异质环境中的个体流动的影响:延迟扩散的SPIR流行病模型
Ghilmana Sarmad1, Salih Djilali2, Soufiane Bentout3
1Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, UAE.
Scientific reports
|August 24, 2025
概括
这项研究引入了一种新的流行病模式, 结果显示,将基本生殖数量降至1以下是疾病灭绝的关键.
科学领域:
- 流行病学
- 数学生物学
- 传染病的发展动态
背景情况:
- 感染的恐惧显著影响了疾病在人群中的传播.
- 以前的模型往往忽略了影响流行病进展的心理因素.
研究的目的:
- 研究一种混合扩散的敏感-受保护-感染-恢复 (SPIR) 流行病模型.
- 使用局部和非局部扩散术语分析感染恐惧的作用.
- 确定疾病灭绝和持续性的值.
主要方法:
- 一个SPIR流行病模型的开发和数学分析.
- 应用混合扩散 (局部和非局部) 来表示恐惧效应.
- 使用变量表达式来导出基本的复制数 (R0).
- 使用Lyapunov函数来建立全球异面稳定性.
主要成果:
- 这种模式被证明具有独特,积极的解决方案.
- 当基本繁殖数 (R0) 低于1时,流行病被证明是灭绝的 (无感染状态的全球无症状稳定性).
- 当R0大于1时,存在感染平衡状态,溶液均持久.
- 使用莱普诺夫函数证明了感染平衡状态的全局异常稳定性.
结论:
- 基本繁殖数 (R0) 是流行病控制的关键值.
- 通过保护措施将R0降低到1以下,对于根除疾病至关重要.
- 这项研究通过量化恐惧和保护的影响, 提供了对疾病控制策略的见解.
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