近年来，受Watts和Strogatz(WS)提出的小世界(SW，Small-World)模型、Barabái和Albert(BA)发现无标度(SF，Scale-Free)特性等两项开创性工作的激发，人们目睹了复杂系统研究领域的巨大进展。复杂网络受到来自控制科学、信息科学、物理学、生物学、数学、经济学等不同学科领域的研究者越来越多的关注，成为当前学术研究的一个热点问题。基于平均场理论，结合计算机数值仿真技术，论文致力于对复杂网络上的传播动力学行为进行分析和研究，内容涉及到复杂网络的宏观结构与疾病的微观感染机制对发生在网络上传染、传播行为的影响，提出具有直接免疫作用的传播模型，以及移动群体环境下的传播行为。论文研究的结果对于深刻理解传染性疾病在社会中的扩散，计算机病毒在互联网上的传播以及大规模连锁故障的发生机理等具有重要的实际意义；对于抑制和抗击新兴传染病和曾出不穷的计算机病毒，制定有效的疾病和计算机病毒的控制策略等具有实际的应用价值。 论文主要创新性工作包括： (1)利用平均场理论和数值仿真相结合的方法，深入分析和研究了一些典型复杂网络模型(如Erdös和Rényi随机图、WS小世界网络、BA无标度网络以及局域世界网络模型)上SIS(Susceptible-Infected-Susceptible)模型的动态传染过程和演化规律。 (2)提出具有直接免疫作用的SIRS(Susceptible-Infected-Susceptible-Removed)模型，基于复杂网络框架，研究了该模型的传染临界特性；另外，提出分阶段传染模型，描述计算机病毒在网络上传播过程，以及安装反病毒软件与部署控制策略对传播过程的影响。 (3)研究几种典型的疾病微观感染机制对传播行为的作用。主要包括：传染延时和局域世界模型参数共同对疾病传染过程的影响；非均匀传染性对无标度网络上SIS传播模型临界阈值的影响；分布式传染速率对复杂网络上SI (Susceptible-Infected)模型的动态传染过程的影响。 (4)分析网络拓扑的动态变化与群体移动对传播行为的影响。基于二维规则晶格，提出新的考虑个体运动的SIS模型和SIR(Susceptible-Infected-Removed)模型，研究个体运动对传播行为的影响，讨论双重时间尺度对动态网络上的传播动力学的作用；提出一个新的动态社区网络模型，并分析该模型上的疾病传播特性。 关键词：复杂网络，随机图，小世界，无标度，局域世界网络，疾病传播，病毒传播，感染机制，传播模型，动态感染过程，临界阈值，预防与控制策略

 Over the past few years, motivated by the seminal works on the small-world effect (SW), which is proposed by Watts and Strogatz (WS), and the scale-free (SF) property, which is found by Barabási and Albert (BA), the great advances in complex systems are witnessed. Complex network has become an important focus among the academic community, which attracts more and more researchers from control theory, information, physics, biology, mathematics, economics etc. In this paper, by combining mean-field theory and computer numerical simulation, the efforts are devoted to the analysis and study of epidemic dynamics on complex networks, which include: the effect of network topological structure and disease infection scheme on the spreading behavior, new epidemic models with direct immunization, and the behavior of epidemic spreading within mobile agents. The results are of high importance to understand the diffusion of infectious disease in the society, the propagation of computer virus on the Internet and the generation mechanism of large-scale cascading failure. The researches are also of real-world application to combat the emerging infectious diseases and various compter viruses, and to design the efficient strategies to control the dissemination of epidemics and computer viruses. The main innovative works and key points are listed as follows: (1)Investigation of the epidemic behavior of SIS (Susceptible-Infected-Susceptible) model on typical complex network models. Combining the mean-field theory and numerical simulations, the dynamical process and evolution of SIS epidemic model on several prototypical complex networks are deeply analyzed and studied, which include random graph of Erdos and Rényi (ER), WS small-world network, BA scale-free network and local-world evolving model. (2)Two improved epidemic models are proposed to study the effect of direct immunization on the spreading behavior. Based on the complex network frameworks, the SIRS (Susceptible-Infected-Susceptible-Removed) model with direct immunization is proposed and the critical characteristics are considered. In addition, a new multi-stage epidemic model is presented to model the competitive processes between the computer virus propagation and anti-virus techniques on the Internet. (3)Research on the influence of various disease infection schemes on the epidemic spreading on complex networks. An improved SIS model with infection delay is proposed to study how the time delay and local-world size affect the epidemic spreading in local-world evolving model. The non-uniform transmission and infection mechanism is introduced into the SIS model and can lead to the non-zero threshold even for the BA scale-free network. The distributed epidemic parameters of modified SI (Susceptible-Infected) model are found to greatly reduce the dynamical evolution of infection density on complex networks. (4)Impact of dynamical topology and mobile agents on epidemic propagation behaviors. Based on the two-dimensional regular lattices, new SIS and SIR (Susceptible-Infected-Removed) model with motion rules, and SIS model with two time-scales are all presented to investigate the effect of the individual's motion on the behavior of epidemic spreading on dynamical topology. At the same tine, a new dynamical network model with community structure is also introduced to perform some analyses and researches about disease spreading characteristics. Key Words: complex network, random graph, small-world, scale-free, local-world evolving network, disease propagation, virus spreading, infection scheme, epidemic model, dynamical infection process, critical threshold, prevention and control strategy