本文選題：復(fù)雜網(wǎng)絡(luò) + 病毒傳播　； 參考：《西南大學》2013年碩士論文

【摘要】：縱觀人類社會發(fā)展史,就是一部人類與各類病毒不斷作戰(zhàn)的抗爭史,從早期的麻疹、天花到近年來的非典型性肺炎以及A(H1N1)型流感,每次流行病的大規(guī)模傳播都給人們的生命和財產(chǎn)帶來巨大的災(zāi)難。此外,隨著信息技術(shù)的發(fā)展,各類網(wǎng)絡(luò)已得到廣泛普及和應(yīng)用,同時計算機病毒借助互聯(lián)網(wǎng)也被迅速的傳播開來,對計算機網(wǎng)絡(luò)安全造成了極大威脅。因此,認識病毒傳播的特征與規(guī)律,并在此基礎(chǔ)上對病毒傳播過程進行建模,預(yù)測其發(fā)展趨勢,分析流行病傳播的原因和關(guān)鍵因素,進而設(shè)計出有效的預(yù)防和控制策略將是反病毒研究的重要領(lǐng)域,具有重要的理論與現(xiàn)實意義。 過去人們主要研究網(wǎng)絡(luò)拓撲結(jié)構(gòu)和網(wǎng)絡(luò)特性對病毒傳播行為的影響,并且一般都是在具有某種特定性質(zhì)的網(wǎng)絡(luò)上進行研究。本文在理解病毒傳播研究現(xiàn)狀和相關(guān)成果的基礎(chǔ)之上,對經(jīng)典的SIRS病毒傳播模型進行改進,并以改進模型為基礎(chǔ)分別分析了該模型在均勻網(wǎng)絡(luò)與非均勻網(wǎng)絡(luò)上的傳播行為,給出了相應(yīng)的傳播臨界值,并且進行了相關(guān)理論的模擬實驗。此外,還對Twitter社交網(wǎng)絡(luò)上輿論傳播行為在廣告宣傳上的應(yīng)用進行了研究,并以真實數(shù)據(jù)進行模擬實驗。具體地,本文主要研究內(nèi)容和成果如下： 1.在典型的SIRS病毒傳播模型的基礎(chǔ)上,研究了一種帶人工免疫的SIRS類的病毒傳播模型,并且給出了該模型的狀態(tài)變遷圖。針對此改進模型,分別研究其在均勻網(wǎng)絡(luò)與非均勻網(wǎng)絡(luò)上的動力學行為,運用平均場理論方法給出相應(yīng)的動力學方程,并分析各自的動力學行為,得出在均勻網(wǎng)絡(luò)中此模型的傳播臨界閡值；同樣得出在非均勻網(wǎng)絡(luò)上的傳播臨界閾值,經(jīng)分析可以看出傳播臨界閾值與網(wǎng)絡(luò)的拓撲結(jié)構(gòu)有關(guān),而與網(wǎng)絡(luò)中個體的性質(zhì)無關(guān)。 2.在上述所提模型的基礎(chǔ)之上,研究了在隨機免疫策略和目標免疫策略兩種不同的人工免疫策略下病毒在網(wǎng)絡(luò)上的傳播情況,并對兩種免疫策略對病毒傳播的影響進行模擬。發(fā)現(xiàn)在均勻網(wǎng)絡(luò)中由于度分布均勻無法適用目標免疫,在病毒傳播過程中如果對網(wǎng)絡(luò)中的個體事先進行隨機免疫,其感染人數(shù)會隨免疫率的增大而減��；在非均勻網(wǎng)絡(luò)中度分布近似擬合于冪率分布,適用隨機免疫策略和目標免疫策略,分析發(fā)現(xiàn),當在同樣的免疫率條件下,對個體進行目標免疫時其最終感染人數(shù)比對個體進隨機免疫時更少。模擬結(jié)果表明,通過人工免疫可以有效降低穩(wěn)態(tài)感染比例,提高系統(tǒng)的傳播閾值,從而有效控制病毒在復(fù)雜網(wǎng)絡(luò)上的傳播。 3.由于現(xiàn)實中的網(wǎng)絡(luò)并不是完全隨機的,也不是只具有單一的小世界特性或是無標度特性,而是可能同時具備隨機特性、小世界特性和無標度特性,為了反映真實網(wǎng)絡(luò)的此種特性,因此本文引入了異質(zhì)網(wǎng)絡(luò)。此網(wǎng)絡(luò)以ER隨機網(wǎng)絡(luò)、WS小世界網(wǎng)和BA無標度網(wǎng)絡(luò)為子網(wǎng)絡(luò),采用隨機規(guī)則將三個子網(wǎng)絡(luò)相互連接形成異質(zhì)復(fù)雜網(wǎng)絡(luò)模型,之后以異質(zhì)網(wǎng)絡(luò)模型的演化算法生成網(wǎng)絡(luò)拓撲結(jié)構(gòu)圖,分析得到相應(yīng)的網(wǎng)絡(luò)特征數(shù)據(jù),并畫出相應(yīng)的度分布曲線圖。再以異質(zhì)網(wǎng)絡(luò)為基礎(chǔ),研究帶人工免疫的SIRS病毒傳播模型在其上的傳播行為,并以A(H1N1)型流感病毒作為異質(zhì)網(wǎng)絡(luò)上傳播的病毒進行仿真模擬實驗。模擬結(jié)果表明,由于異質(zhì)網(wǎng)絡(luò)的異質(zhì)性,在病毒傳播過程中進行人工免疫時,最終感染人數(shù)的比例比在只具有單一特性的網(wǎng)絡(luò)上大大降低,人工免疫效果更加明顯。 4. Twitter社交網(wǎng)絡(luò)作為新興的交流工具,其上的信息傳播具有普及廣和速度快的特點,粉絲轉(zhuǎn)發(fā)感興趣的消息是一種普遍的現(xiàn)象,所以在Twitter社交網(wǎng)絡(luò)上進行廣告宣傳對企業(yè)來說具有很大的吸引力。首先利用SQL Server軟件對2012年部分Twitter社交網(wǎng)絡(luò)數(shù)據(jù)進行分析,得出該網(wǎng)絡(luò)具有無標度特性,并畫出度分布曲線圖。然后在復(fù)雜網(wǎng)絡(luò)中SIR輿論傳播模型的基礎(chǔ)之上對Twitter社交網(wǎng)絡(luò)上的廣告宣傳進行分析,得出最終知道消息人群的密度與網(wǎng)絡(luò)的度分布相關(guān)。模擬結(jié)果表明,由于Twitter社交網(wǎng)絡(luò)度分布近似于冪率分布,所以其網(wǎng)絡(luò)中存在部分度很大的節(jié)點,即某些個體擁有數(shù)目較多的粉絲數(shù),如果企業(yè)雇傭此類人群在社交網(wǎng)絡(luò)上進行廣告宣傳,則其效果比只雇傭一般個體的效果更好,能在更短的時間內(nèi)讓廣告覆蓋整個社交網(wǎng)絡(luò)。據(jù)此,可以為企業(yè)提供廣告投放建議,使其以較小的成本獲得較大的廣告宣傳效應(yīng)。
[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.
【學位授予單位】：西南大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：TP393.08;O157.5

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