Collaborative Research: Modeling the Spatial and Temporal Dynamics of Vector-borne Diseases in Florida: The Case of Zika Outbreak in 2016

该项目将开发数学模型，以研究寨卡病毒引入佛罗里达南部的动态。 研究人员将对这些模型进行数学、统计和计算分析，以更好地了解影响寨卡病毒地理传播的因素。登革热、基孔肯雅热和寨卡等几种病媒传播的疾病已传入佛罗里达，造成当地疫情（2009-2010年和2013年的登革热，2014年的基孔肯雅热，2016年的寨卡），并造成重大的公共卫生问题。登革热、基孔肯雅热和寨卡病毒都有相同的主要蚊子传播媒介--埃及伊蚊和白纹伊蚊，这两种蚊子在佛罗里达都很丰富，能够传播其他几种疾病。这些VBDs的传播周期受到季节变化、气候条件和人类活动的严重影响。根据2016年迈阿密海滩、温伍德和佛罗里达的小河寨卡疫情的数据，他们将建立和校准包括宿主和媒介的年龄结构以及季节性影响的模型，以研究寨卡在佛罗里达的时空动态和传播。其目标是更好地准备预测和应对类似的重新出现的虫媒病毒，如登革热，基孔肯雅和黄热病病毒。该项目涉及研究生和博士后培训生，其结果将通过研讨会、会议演示和期刊出版物传播。该项目的目标是：（i）由于登革热、基孔肯雅和寨卡病毒在时空分布上具有显著的一致性，研究人员将开发一个多尺度（多区域）多斑块模型来研究VBD的地理传播。大尺度用于描述人类从区域到区域的长距离移动，小尺度用于模拟蚊子和人类在区域内从斑块到斑块的短距离移动。该模型将用于模拟2016年寨卡病毒在迈阿密海滩、温伍德和利特尔里弗的地理和局部传播，并将采用多尺度分析和慢-快动力系统理论进行研究。(ii)由于病媒和宿主的年龄分布对VBD的传播非常重要，研究员将构建年龄结构模型，研究蚊子和人类的年龄分布对VBD传播的影响，并使用模型设计最佳病媒控制政策和评估不同年龄组的疾病风险。(iii)由于年龄结构模型可以写成Banach空间中的抽象方程，并且季节性施加了自然的时间周期，因此PI将研究半线性周期方程的非线性动力学，并将结果应用于具有季节变化的年龄结构VBD模型。研究半线性周期柯西问题周期解的非线性动力学性质具有重要意义，因为所得结果对于研究周期时滞方程模型、时间周期反应扩散方程、年龄-该奖项反映了NSF的法定使命，并被认为值得通过利用基金会的知识价值和更广泛的影响进行评估来支持审查标准。

This project will develop mathematical models to study the dynamics of Zika virus introduced to southern Florida. The investigators will carry out mathematical, statistical and computational analyses of these models to better understand factors affecting the geographical spread of Zika. Several vector-borne diseases (VBDs), such as dengue, chikungunya and Zika, have been imported into Florida, caused local outbreaks (dengue in 2009-2010 and 2013, chikungunya in 2014, Zika in 2016), and posed major public health problems. Dengue, chikungunya and Zika share the same primary mosquito vectors, Aedes aegypti and Aedes albopictus, both abundant in Florida and capable of transmitting several other diseases. The transmission cycle of these VBDs is heavily influenced by seasonal changes, climate conditions, and human movement. Based on data from 2016 Zika outbreaks in Miami Beach, Wynwood, and Little River in Florida, they will build and calibrate models including the age structure of both hosts and vectors as well as the effects of seasonality to study the spatial and temporal dynamics and spread of Zika in Florida. The objectives are to be better prepared to anticipate and respond to similar reemerging arboviruses such as dengue, chikungunya and yellow fever viruses. The project involves graduate students and postdoctoral trainees and results will be disseminated through seminars, conference presentations and journal publications.The goals of this project are: (i) Since dengue, chikungunya and Zika viruses have significant agreement in their spatiotemporal distributions, the PIs will develop a multi-scale (multi-region) multi-patch model to study the geographical spread of VBD. A large scale is used to describe the long distance human movement from regions to regions and a small scale is used to model the short distance movement of both mosquitoes and humans from patches to patches within a region. The model will be applied to simulate the geographical and local spread of Zika among Miami Beach, Wynwood, and Little River in 2016 and will be studied employing multiple scale analysis and slow-fast dynamical system theory. (ii) Since age distributions of both vectors and hosts are very important in the spread of VBD, the PIs will construct age-structured models to study the effect of age distributions of both mosquitoes and humans on the transmission of VBD and use the model to design optimal vector control policies and to access disease risk for different age groups. (iii) Since age-structured models can be written as abstract equations in Banach spaces and seasonality imposes a natural temporal period, the PIs will study the nonlinear dynamics of semilinear periodic equations and apply the results to age-structured VBD models with seasonal change. Studying the nonlinear dynamics of periodic solutions in the semilinear periodic Cauchy problem will be transformative since the results will be useful in studying periodic delay equation models, time-periodic reaction-diffusion equations, and age-structured periodic models arising from biology and epidemiology.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.