复杂性科学和复杂网络是近几年科学领域研究的热点，更是融合了物理、数学、计算机科学、生物学、社会学等多领域研究方法的交叉性学科，复杂性科学和复杂网络的研究也推动了人类对于各种社会问题研究的进步。人类社会的许多现象和事实都可以抽象为一定的网络模型，然后借助复杂网络的研究方法展开研究，例如航空网、铁路网、食物链网、基因调控网等。通过对实际网络的研究，学者们发现现实中的网络具有小世界和无标度的特性，从而推动了复杂网络模型理论的发展进步，从最初的规则网络模型到小世界网络模型和无标度网络模型，再到适应性网络模型和空间网络模型等。复杂网络的研究主要分为两大类，一大类是研究网络本身的特性和网络模型，如对社团结构的划分等，另一大类是借助复杂网络模型和研究方法研究动力学，包括网络本身的动力学和网络上的动力学，如适应性网络模型、传染病传播、随机游走等。动力学的研究试图解决传染病传播、交通拥堵、舆论传播、投资理财等贴近生活的各种问题。本文研究复杂网络上的动力学，主要的研究对象是传染病的传播。本论文借鉴已有的研究成果，对传染病传播模型进行了完善，以“潜伏期”机制和“适应性”机制作为研究的创新点，研究的主要内容包括：第一，研究适应性网络上具有潜伏期机制的传染病传播；在这一方面的研究中，以Gross等人[1]的研究作为基础，在适应性的网络上选取SIS模型作为研究对象，在传播的过程中加入“潜伏期”机制，即将染病的人群细分为两类，一类是表现出病症的显性染病的人群，一类是已经染病却没有表现病症的隐性染病的人群，主要讨论“潜伏期”机制对传染病传播过程的影响，得出在同等“断边重连”概率条件下，没有潜伏期机制的传播要比有潜伏期机制的传播感染的人数更多等结论；第二，研究加权网络上具有潜伏期机制的适应性传染病传播；在这一方面的研究中，主要考虑的是传染病在社会上的传播强度会由于人与人之间关系的亲密程度不同而不同。传染病在人与人之间传播强度并不相同，将研究引入到加权网络上（本文研究加边权的情况）进行研究，通过权重来形象的表示人与人之间关系的亲密程度；通过个体的主观能动性来改变个体之间联系的权重，从而达到“适应性”机制的目的，主要讨论“适应性”即权重的改变对传染病传播过程的影响，在研究中找到了 状态的相图，通过对相图上点的研究找寻演化终止后权重分布发生变化的规律；第三，以生活中比较熟悉的HIV病毒作为一个例子，研究动态社会网络中的传染病传播；这一部分通过具有“适应性”机制和“潜伏期”机制的传播模型来模拟HIV病毒的传播，根据HIV病毒的特性设定模型中的参数，通过分析模拟传播结果给出预防HIV病毒传播的建议。最后，就本文几方面的工作进行了总结，对未来可以继续研究的内容做了展望，并对在攻读硕士研究生期间给予我帮助的人们表示最衷心地感谢。

Complex Sciences and Complex Networks are popular in recent years. The way of research contains the knowledge of physics, mathematics, computer science, ecology, social science etc., which makes a great improvement to the solution of different kinds of social problems.Many phenomena and events of human society can be extracted into a complex network model. Throughout the research of real networks, like airline networks, railway networks, food chain networks and gene regulation networks, researchers find the small world and scale-free properties of real network by using the methods of complex networks. These properties develop the complex networks models, from the origin regular networks to small-world networks, scale-free networks, adaption networks and even spatial networks.The research of complex networks can be divided into two aspects. The first one studies the property of networks itself and the network models, like community structure and synchronization etc. The second one studies the dynamics of the networks and the dynamics on the networks, such as epidemic transmission and random walking etc. The research of dynamics tries to solve the problems in real life, like epidemic transmission, traffic jams, rumor transition, investment and financing. This paper mainly studies the dynamic of epidemic transmission on the complex networks. Having consulted the existed achievements, I improve the epidemic transmission model by adding incubation and adaption mechanism. The research contains the following parts.Firstly, I study the epidemic transmission with incubation mechanism on adaption networks. In this part, on the basis of Gross’ work, I also study the SIS model on adaption networks. At the same time, I add incubation mechanism to the model, which means some people who get infected can still act as a normal one in a special period. I mainly discuss the influence of incubation mechanism during the time of epidemic transmission.Secondly, I study the epidemic transmission with incubation and adaption mechanism on weighted networks. In this part, I consider the extent of people’s relationship, which will influence the strength of infection. I use the weight of the edge to represent people’s relationship. The adaption mechanism can be realized by people who subjectively change the weight with his neighbors. I mainly focus on the influence of weight changing during the epidemic transmission.Thirdly, I use HIV virus as an example to study the epidemic transmission on dynamic social networks. In this part, I build a model with incubation and adaptive mechanism to simulate the transmission of HIV virus. The parameters in the model are set based on the property of HIV virus. I give some advice to take precautions against HIV virus according to the model results.Finally, I draw the conclusion of the whole paper, list the content I can continue to do in the future and acknowledge those who help me a lot during my graduate study.