时滞和动态网络对传染病传播动力学性态及防控的影响研究

项目名称： 时滞和动态网络对传染病传播动力学性态及防控的影响研究

项目编号： No.11201135

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 邹劭芬

作者单位： 湖南大学

项目金额： 22万元

中文摘要： 鉴于目前仓室传染病模型和无标度网络传染病模型存在一定局限，针对传染病潜伏期和网络动态变化的客观存在性及其对传染病传播动态的本质影响，本项目量化潜伏期为时滞、量化网络动态为指数变动的幂率分布，分别建立时滞无标度网络传染病模型和动态无标度网络传染病模型，借助数学理论工具和数值计算定性定量地分析时滞网络模型、动态网络模型的动力学性态，分别得出时滞、网络动态与传染病传播阈值、传播强度、高峰次数强度、传染病持久性及最终规模的内在定性定量关系，利用数值仿真检验理论结果，对比已有无标度网络模型的所获结果进而讨论引入时滞、网络动态的合理性。对上述所建两类网络模型，引入防控项，比较均匀防控策略与目标防控策略，为传染病的有效防控策略提供合理建议。将本项目所获理论应用于具体疾病SARS，根据疾病的流行数据获取恰当时滞和指数参数值，给出其传播阈值、传播强度和高峰次数强度及到达时间等，为疾病防控策略提供理论指导。

中文关键词： 传染病模型；复杂网络；传播动力学；时滞；动态结构

英文摘要： Based on advantages and disadvantages of classic compartmental epidemic models and scale-free network epidemic models, we consider the effects on epidemic dynamics of latency and varying network structure. We quantify the latency and varying network structure to build delayed epidemic models on scale-free networks and epidemic models on scale-free networks with varying exponent. With the help of theoretical tools and numerical simulations, we study their dynamics quantitatively and qualitatively. We first obtain results to reveal the intrinsic connection of latency and varying network structure with the threshold of epidemics, outbreak strength and number, persistence, and final size. We then demonstrate the theoretical results with numerical simulations and further discuss the reasonability of introducing latency and varying exponent. In order to provide valid prevention and control strategies, we shall compare the effects of random control strategy and targeted control strategy. As an application, the obtained results will be verified by SARS.

英文关键词： Epidemic models；Complex networks；Transmission dynamics；Delay；Variable structure