标题： 关于巴西与佛罗里达之间登革热地理传播的研究：具有时间延迟的多斑块模型 显示英文标题

标题： On the Geographic Spread of Chikungunya between Brazil and Florida: A Multi-patch Model with Time Delay

摘要： 基孔肯雅热（CHIK）是一种通过感染基孔肯雅病毒（CHIKV）的{\it 埃及伊蚊}蚊子叮咬传播给人类的病毒性疾病。 在过去的十年中，由于迈阿密作为国际旅行枢纽的关键位置，特别是从中美洲和南美洲包括巴西等地进口的CHIKV，每年都会将CHIKV带入佛罗里达州。 这项工作研究了CHIK的地理传播，结合了人类流动、温度依赖性以及垂直传播和不同区域的潜伏期等因素。 该模型的核心是多区域框架的整合，在数值分析中考虑了从流行巴西州到佛罗里达州的人类流动。 我们建立了蚊子繁殖数$\mathcal{R}_{m}$与疾病繁殖数$\mathcal{R}_{0}$之间的重要关联，以及在多区域环境中疾病动态的关系，不仅包括数值分析，还从理论角度进行了探讨。 通过用真实人口和温度数据验证的数值模拟，可以理解在许多不同情景下的疾病动态，并进行未来预测，为潜在的有效控制策略提供见解，同时解决这些策略应何时采用的问题。 显示英文摘要

摘要： Chikungunya (CHIK) is a viral disease transmitted to humans through the bites of {\it Aedes} mosquitoes infected with the chikungunya virus (CHIKV). CHIKV has been imported annually to Florida in the last decade due to Miami's crucial location as a hub for international travel, particularly from Central and South America including Brazil, where CHIK is endemic. This work addresses to the geographic spread of CHIK, incorporating factors such as human movement, temperature dependency, as well as vertical transmission, and incubation periods, for different patches. Central to the model is the integration of a multi-patch framework, and in the numerical analysis it is considered human movement between endemic Brazilian states and Florida. We establish crucial correlations between the mosquito reproduction number $\mathcal{R}_{m}$ and the disease reproduction number $\mathcal{R}_{0}$ with the disease dynamics in a multi-patch environment, encompassing not only a numerical analysis but also from a theoretical perspective. Through numerical simulations, validated with real population and temperature data, it is possible to understand the disease dynamics under many different scenarios and make future projections, offering insights for potential effective control strategies, as well as addressing the timing for these strategies to be adopted.