复杂网络上流行病传播动力学行为及其免疫控制策略研究

发布时间：2018-07-02 10:10

本文选题：复杂网络 + 病毒传播　；参考：《西南大学》2013年硕士论文

【摘要】：纵观人类社会发展史,就是一部人类与各类病毒不断作战的抗争史,从早期的麻疹、天花到近年来的非典型性肺炎以及A(H1N1)型流感,每次流行病的大规模传播都给人们的生命和财产带来巨大的灾难。此外,随着信息技术的发展,各类网络已得到广泛普及和应用,同时计算机病毒借助互联网也被迅速的传播开来,对计算机网络安全造成了极大威胁。因此,认识病毒传播的特征与规律,并在此基础上对病毒传播过程进行建模,预测其发展趋势,分析流行病传播的原因和关键因素,进而设计出有效的预防和控制策略将是反病毒研究的重要领域,具有重要的理论与现实意义。过去人们主要研究网络拓扑结构和网络特性对病毒传播行为的影响,并且一般都是在具有某种特定性质的网络上进行研究。本文在理解病毒传播研究现状和相关成果的基础之上,对经典的SIRS病毒传播模型进行改进,并以改进模型为基础分别分析了该模型在均匀网络与非均匀网络上的传播行为,给出了相应的传播临界值,并且进行了相关理论的模拟实验。此外,还对Twitter社交网络上舆论传播行为在广告宣传上的应用进行了研究,并以真实数据进行模拟实验。具体地,本文主要研究内容和成果如下： 1.在典型的SIRS病毒传播模型的基础上,研究了一种带人工免疫的SIRS类的病毒传播模型,并且给出了该模型的状态变迁图。针对此改进模型,分别研究其在均匀网络与非均匀网络上的动力学行为,运用平均场理论方法给出相应的动力学方程,并分析各自的动力学行为,得出在均匀网络中此模型的传播临界阂值；同样得出在非均匀网络上的传播临界阈值,经分析可以看出传播临界阈值与网络的拓扑结构有关,而与网络中个体的性质无关。 2.在上述所提模型的基础之上,研究了在随机免疫策略和目标免疫策略两种不同的人工免疫策略下病毒在网络上的传播情况,并对两种免疫策略对病毒传播的影响进行模拟。发现在均匀网络中由于度分布均匀无法适用目标免疫,在病毒传播过程中如果对网络中的个体事先进行随机免疫,其感染人数会随免疫率的增大而减小；在非均匀网络中度分布近似拟合于幂率分布,适用随机免疫策略和目标免疫策略,分析发现,当在同样的免疫率条件下,对个体进行目标免疫时其最终感染人数比对个体进随机免疫时更少。模拟结果表明,通过人工免疫可以有效降低稳态感染比例,提高系统的传播阈值,从而有效控制病毒在复杂网络上的传播。 3.由于现实中的网络并不是完全随机的,也不是只具有单一的小世界特性或是无标度特性,而是可能同时具备随机特性、小世界特性和无标度特性,为了反映真实网络的此种特性,因此本文引入了异质网络。此网络以ER随机网络、WS小世界网和BA无标度网络为子网络,采用随机规则将三个子网络相互连接形成异质复杂网络模型,之后以异质网络模型的演化算法生成网络拓扑结构图,分析得到相应的网络特征数据,并画出相应的度分布曲线图。再以异质网络为基础,研究带人工免疫的SIRS病毒传播模型在其上的传播行为,并以A(H1N1)型流感病毒作为异质网络上传播的病毒进行仿真模拟实验。模拟结果表明,由于异质网络的异质性,在病毒传播过程中进行人工免疫时,最终感染人数的比例比在只具有单一特性的网络上大大降低,人工免疫效果更加明显。 4. Twitter社交网络作为新兴的交流工具,其上的信息传播具有普及广和速度快的特点,粉丝转发感兴趣的消息是一种普遍的现象,所以在Twitter社交网络上进行广告宣传对企业来说具有很大的吸引力。首先利用SQL Server软件对2012年部分Twitter社交网络数据进行分析,得出该网络具有无标度特性,并画出度分布曲线图。然后在复杂网络中SIR舆论传播模型的基础之上对Twitter社交网络上的广告宣传进行分析,得出最终知道消息人群的密度与网络的度分布相关。模拟结果表明,由于Twitter社交网络度分布近似于幂率分布,所以其网络中存在部分度很大的节点,即某些个体拥有数目较多的粉丝数,如果企业雇佣此类人群在社交网络上进行广告宣传,则其效果比只雇佣一般个体的效果更好,能在更短的时间内让广告覆盖整个社交网络。据此,可以为企业提供广告投放建议,使其以较小的成本获得较大的广告宣传效应。
[Abstract]:The history of human social development is a history of fighting between human and various viruses. From the early measles, smallpox to the atypical pneumonia in recent years and the A (H1N1) influenza, the massive spread of each epidemic has brought great disaster to people's lives and property. In addition, with the development of information technology, various kinds of networks It has been widely popularized and applied. At the same time, the computer virus has been spread rapidly with the help of the Internet, causing a great threat to the security of the computer network. Therefore, the characteristics and laws of the virus transmission are recognized. On the basis of this, the virus propagation process is modeled, the development trend is predicted, the causes and key points of the epidemic spread are analyzed. Therefore, designing effective prevention and control strategies will be an important field of anti-virus research, and have important theoretical and practical significance.
In the past, people mainly studied the impact of network topology and network characteristics on virus propagation behavior, and generally studied on a network with certain specific properties. Based on the understanding of the current situation of virus transmission and related achievements, this paper improved the classic SIRS virus propagation model and based on the improved model. Based on the analysis of the propagation behavior of the model on uniform network and non-uniform network, the corresponding propagation critical value is given, and the simulation experiments of the related theories are carried out. In addition, the application of public opinion propagation in the Twitter social network is studied, and the simulation experiments are carried out with real data. The main contents and results of this paper are as follows:
1. on the basis of the typical SIRS virus propagation model, a virus propagation model of SIRS class with artificial immunity is studied, and the state transition diagram of the model is given. The dynamic behavior of the model is studied on the uniform network and inhomogeneous network, and the corresponding dynamics is given by means of the mean field theory. The propagation critical threshold of the model in a uniform network is obtained, and the critical threshold of propagation on a non-uniform network is obtained. It can be seen that the critical threshold of propagation is related to the topology of the network, but is independent of the nature of the individual in the network.
2. on the basis of the above mentioned model, the spread of the virus on the network under the two different artificial immune strategies of the random immunization strategy and the target immunization strategy was studied, and the effects of the two immune strategies on the transmission of the virus were simulated. In the process of virus transmission, if the individuals in the network are immunized in advance, the number of infected people will decrease with the increase of the immune rate; the moderate distribution of the non-uniform network is approximated to the power rate distribution, and the random immunization strategy and the target immunization strategy are applied. The number of final infection is less than that of the random immune system. The simulation results show that the ratio of steady state infection can be reduced effectively by artificial immunity and the transmission threshold of the system can be improved, thus effectively controlling the spread of the virus on the complex network.
3. because the network in reality is not completely random, nor is it only a single small world characteristic or scale-free characteristic, it may have random properties, small world characteristics and scale-free properties. In order to reflect the characteristics of real networks, this paper introduces heterogeneous networks. This network is based on ER random network, WS small world. The network and BA scale-free network are subnetworks. The three sub networks are connected by random rules to form a heterogeneous complex network model. After that, the network topology graph is generated by the evolutionary algorithm of heterogeneous network model. The corresponding network feature data are obtained and the corresponding degree distribution curves are drawn. Based on the heterogeneous network, the research belt is studied. The propagation behavior of the SIRS virus propagating model on the artificial immune system and the A (H1N1) influenza virus as the virus transmitted on the heterogeneous network are simulated. The simulation results show that the proportion of the final infection number is only single, because of the heterogeneity of the heterogeneous network. The network of sex is greatly reduced, and the effect of artificial immunity is more obvious.
4. Twitter social network, as a new communication tool, has the characteristics of spread and fast speed, and the message that fans are interested in is a common phenomenon. So advertising on Twitter social networks is very attractive to enterprises. First of all, the use of SQL Server software for partial Twi in 2012 Tter social network data is analyzed, and the network has no scaling characteristics, and the degree distribution curve is drawn. Then, on the basis of the SIR public opinion propagation model in the complex network, the advertisement publicity on the Twitter social network is analyzed. The conclusion is that the density of the message crowd is related to the degree distribution of the network. The simulation results show that the network is related to the degree distribution of the network. Because the degree distribution of the Twitter social network is similar to the power rate distribution, there is a large number of nodes in the network, that is, some individuals have a large number of fans. If the enterprise employs such people to advertise on social networks, the effect is better than only a single individual, and can be made in a shorter time. Advertising covers the whole social network. Accordingly, it can provide advertising suggestions for enterprises, so that they can get a larger advertising effect at a lower cost.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：TP393.08;O157.5

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