发表机构
Yangzhou University; York University（扬州大学; 约克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出带移动边界的非局部登革热模型，纳入干湿季节与脉冲干预，通过广义主特征值获得扩散-消亡判据，数值模拟显示短旱季难控病、强脉冲干预增效。
AI 中文摘要
季节更替和人为干预深刻影响登革热的传播，且人类和蚊媒均可进行长距离扩散。本文提出了一个具有移动边界的非局部反应扩散登革热模型，该模型融入了干湿季节性和脉冲干预。我们首先给出了模型全局解的存在唯一性，然后引入了广义主特征值的定义，并利用分离变量法证明了当核函数相同时该特征值的唯一性，进而讨论了其相关性质。以该特征值作为指标，我们获得了扩散-消亡二分性，并推导出分别刻画扩散状态和消亡状态的两个判据。我们的结果推广了无脉冲干预的非局部扩散模型以及有脉冲干预但无季节更替的模型。最后，我们通过数值模拟验证了理论发现，并探究了各种因素对登革热传播的影响。数值结果表明，较短的旱季使疾病控制更加困难，而更强化的脉冲干预则能提升控制效果。
英文摘要
Seasonal succession and human intervention profoundly influence dengue fever transmission, and both humans and mosquito vectors can disperse over long distances. This paper proposes a nonlocal reaction-diffusion dengue model with moving boundaries that incorporates dry-wet seasonality and impulsive intervention. We first present the existence and uniqueness of the global solution to the model, then introduce the definition of the generalized principal eigenvalue, prove its uniqueness when the kernel functions coincide via the method of separation of variables, and further discuss its associated properties. Using this eigenvalue as an index, we obtain a spreading-vanishing dichotomy and derive two criteria that characterize the spreading and vanishing states, respectively. Our results extend both the nonlocal diffusion model without impulsive intervention and the model with impulsive intervention but without seasonal succession. Finally, we validate our theoretical findings and investigate how various factors affect dengue transmission through numerical simulations. The numerical results indicate that a shorter dry season makes disease containment more difficult, whereas more intensive impulsive intervention enhances control efficacy.
