延迟流行病模型是由潜伏,感染和免疫持续时间决定的
Masoud Saade1, Samiran Ghosh2, Malay Banerjee2
1Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia.
Mathematical biosciences
|February 5, 2024
概括
我们开发了新的流行病模型,使用延迟微分方程来研究疾病传播. 我们的模型表明,菌株之间的竞争如何导致振荡,影响疾病动态.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 动态系统 动态系统
背景情况:
- 了解传染病的动态对于公共卫生至关重要.
- 之前的模型往往简化了疾病状态之间的复杂过渡.
- 疾病进展的时间延迟显著影响流行病轨迹.
研究的目的:
- 采用延迟微分方程引入新的单株和双株流行病模型.
- 分析流行病模型的稳定性,了解菌株竞争.
- 调查导致疾病流行率周期性波动的条件.
主要方法:
- 制定流行病模型作为延迟微分方程系统.
- 证明模型解决方案的存在和积极性.
- 将延迟微分方程减少为稳定性分析的积分方程.
- 研究静态解决方案及其稳定性标准.
主要成果:
- 对于提出的模型的解决方案的存在和积极性是数学证明的.
- 对静止溶液的分析表明,具有更高基本繁殖数量的菌株通常占主导地位.
- 超过临界基本繁殖数量可能会破坏静止溶液的稳定性,导致两种菌株共存的周期性振荡.
- 在振荡模式中的模型动态取决于超出基本复制数的参数.
结论:
- 延迟微分方程为模拟流行病动态提供了一个强大的框架.
- 压力竞争可能导致复杂的,非直观的动态,包括周期性振荡.
- 这些发现提供了关于多菌株传染病传播的见解,对季节性流感模式有影响.
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