周期变化环境中具有脉冲干预的登革热模型

中文摘要 AI 辅助

脉冲干预是一种高效的感染控制措施，因为它通过短期行动影响疾病传播。此外，登革热媒介和宿主的栖息地范围因环境和气候因素而呈现周期性变化。为了研究脉冲干预和区域演化对疾病传播的影响，我们提出了一个在周期性变化区域中包含脉冲扰动的登革热反应扩散模型。通过应用庞加莱映射和Krein-Rutman定理，我们建立了具有脉冲的周期特征值问题主特征值的存在性，从而扩展了先前关于固定区域中无脉冲效应的反应扩散方程的研究。利用比较原理和单调迭代理论，推导了周期解长期动态的充分条件。数值模拟证实了理论发现，并阐明了脉冲干预强度和周期性区域演化对疾病传播模式的影响。我们的结果表明，增加脉冲干预的强度抑制疾病传播，而区域变化的幅度较大则阻碍疾病控制。

英文摘要

Pulse interventions represent a highly effective measure for infection control, as they influence disease transmission through short-term actions. In addition, the habitat ranges of dengue vectors and hosts exhibit periodic variations driven by environmental and climatic factors. To investigate the effects of impulsive interventions and domain evolution on disease transmission, we propose a dengue fever reaction-diffusion model that incorporates impulsive perturbations in a periodically varying domain. By applying the Poincar$\acute{e}$ map and the Krein-Rutman theorem, we establish the existence of the principal eigenvalue for the periodic eigenvalue problem with impulses, thereby extending previous studies on reaction-diffusion equations in fixed domains without impulsive effects. Sufficient conditions governing the long-term dynamics of periodic solutions are derived using the comparison principle and monotone iteration theory. Numerical simulations corroborate the theoretical findings and elucidate the effects of impulsive-intervention intensity and periodic domain evolution on disease transmission patterns. Our results indicate that increasing the intensity of pulse interventions suppresses disease transmission, whereas a larger magnitude of domain variation impedes disease control.

发表机构

• School of Mathematical Science, Yangzhou University（扬州大学数学科学学院）
• Department of Applied Mathematical Sciences, Korea University（韩国大学应用数学科学系）

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