• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Rumor Spreading Model with Immunization Strategy and Delay Time on Homogeneous Networks?

    2017-05-09 11:46:47JingWang王靜YaQiWang王亞奇andMingLi李敏
    Communications in Theoretical Physics 2017年12期
    關(guān)鍵詞:王靜李敏

    Jing Wang(王靜)Ya-Qi Wang(王亞奇)? and Ming Li(李敏)

    1Xi’an Research Institute of Hi-Tech,Xi’an 710025,China

    2Department of Electronics Technology,Engineering University of the Chinese People’s Armed Police Force,Xi’an 710086,China

    1 Introduction

    Rumors have a long history,usually referring to the fabricated opinion on public affairs.[1?2]Traditional rumors spread from mouth to mouth.In recent years,with the rapid development of various social networks,rumors can quickly propagate by means of social networks,[3?4]which usually be called Internet rumors.Traditional rumors,especially Internet rumors,not only interfere with people’s daily lives,but even endanger the stability of society.[5?7]Therefore,it is of great theoretical signi ficance to explore the inherent propagation mechanism of rumors,and this has already aroused a widespread concern of many researchers both at home and abroad.

    As early as the 1940s,sociologists began to study the spread of rumors.However,the modeling of rumor propagation began in 1965,when Daley and Kendall[8]introduced the first rumor spreading model,which is called the DK model.In the DK model,the population was divided into three categories:people who do not contact the rumor,people who have accepted the rumor and spread it,and people who have accepted the rumor but do not propagate it again.The classical DK model laid a foundation for the following research.The effect of the topological properties of networks on the spread of rumors was investigated by Sudbury.[9]Subsequently,with the development of complex network propagation theory,Zanette[10]applied the theory to construct a rumor-spread model,and discussed the propagation characteristics of the model on small-world networks.Based on the susceptible-infectedremoved(SIR)model used to describe the spreading process of epidemics,[11?13]Morenoet al.[14]built an SIR rumor propagation model,but where“S” represents“ignorants” who have no idea about the rumor,“I” stands for“spreaders” who contact the rumor and spread it,and“R”represents “sti flers” who contact the rumor but do not propagate it.According to this SIR model,researches proposed many similar rumor-spread models.One of the most widely used SIR rumor model was presented by Nekoveeet al.[15]They considered the forgetting during the spreading process of rumors as an important mechanism,and constructed the mean- field equations in both homogeneous networks and heterogeneous networks.The critical thresholds and the final degree of rumor spreading on the two different types of networks were obtained.For more research on rumors,including Internet rumors,refer to Refs.[16–23].

    In view of the spread of rumors can cause a lot of harm,and drawing experience from the immunization strategies for the prevention of epidemic transmission,[24]it has important realistic meaning to adopt immunization strategies to control rumor spreading,which has attracted attention of the relevant researchers.Huanget al.[25]ap-plied two major immunization strategies on the smallworld network.They found that the size of the average degree of the network determined the immune effect of the two immunization strategies.In addition,they also proposed a strategy to prevent the spread or rumors.In order to deal with rumor propagating on the mobile social networks,two kinds of methods have been designed,i.e.,blocking in fluential nodes to spread rumors and clarifying rumors by spreading truth.[26]Incorporating the two kinds of methods,Heet al.[27]presented two cost-efficient strategies to restrain rumor spreading on the mobile social networks.The efficiency of the two strategies had been extensively evaluated.Zhaoet al.[28]introduced the immunization strategy into the rumor spreading on the homogeneous networks.They obtained an immunization threshold value,above which rumor spreading can be stopped.They also found that the average degree of the network greatly in fluences the spread of rumors.In this paper,the immunization strategies all refer to make people know the truth of rumors.

    In the above models,the immunization strategies are assumed to be implemented just when there are rumors spreading on the networks.In fact,the spread of rumors is always ahead of the implementation of immunization strategies,i.e.,there must be a delay time between them.How will the delay time together with the spread of the truth affect the immune effect? It is clear that the research of this problem will enable us to grasp more realistic dynamical behaviors of rumor spreading on the networks that are implemented immunization strategies,so that we can take measures to improve the immune effect of the corresponding immunization strategies.However,to the best of our knowledge,up to now,the above problem has not yet been explored.In order to efficiently prevent and control rumor propagation,considering the in fluence of the delay time before implementing immunization strategy and the spread of the truth of rumors,this paper proposes a novel SIR rumor model.The propagation characteristics of the model are fully examined by the detailed theory analysis and the sufficient numerical simulations.As will be shown in Sec.4,the delay time and the truth propagation have a great in fluence on the propagation dynamical behaviors of rumors.

    2 SIR Rumor Spreading Model

    Consistent with the previous research,[14]in our SIR rumor spreading model,the total population consisting ofNindividuals are also divided into ignorants(denoted asS),spreaders(denoted as I)and sti flers(denoted asR),which with respect to the epidemic correspond to susceptible individuals,infected individuals and removed individuals,respectively.In this paper,it is assumed that the population are closed and mixed,and can be described by using the homogeneous networks.In order to control the rumor spreading,the random immunization strategy that randomly chooses a part of ignorants and makes them know the truth of rumors is adopted.Considering the existence of delay time,thefpercent of ignorants in the entire network are randomly chosen to implement immunization afterTtime steps of rumor spreading.Different from the immune mechanism in the spread of epidemics,the immunized nodes here not only oppose the spread of rumors,but also can propagate the truth of rumors to spreaders.Of course,these immunized nodes will not accept rumors and thus can be classi fied as sti flers.So,stiflers in this paper consist of two different types of nodes,one is that who has accepted the rumor but has ceased to spread it(denoted asR1 sti flers),and the other is that who has known the truth of rumors and will propagate it to spreaders,i.e.,the immunized nodes(denoted asR2 sti flers).In the following process of rumor spreading,R1 sti flers will always remain silent state,and are no longer affected by rumors or the truth.So,there is no interaction betweenR1 sti flers andR2 sti flers.In addition,the mechanism that when contacting anR1 sti fler,a spreader will become anR1 sti fler is ignored.This is because thatR1 sti flers do not spread rumors and are likely to just keep silence,which cannot make a spreader into anR1 sti fler.Rumors spread among different nodes through direct contacts.The spreading process of our SIR rumor model is given as Fig.1.

    Fig.1 The rumor propagation process of our SIR model.

    Combining with Fig.1,the transmission laws of our SIR model are as follows:

    (i)When an ignorant contacts a spreader,the ignorant will become a spreader with probabilityλ(called the effective propagation rate),or anR1 sti fler at a rateγdue to he/she owning a strong identification force.

    (ii)When a spreader contacts anR2 sti fler from theT+1 time step,the spreader will become anR2 sti fler with the probabilityα(called the reliability of the truth).

    (iii)If a spreader contacts another spreader,the initiating one will become anR1 sti fler with probabilityσ.

    (iv)Due to forgetting or disinclination to spread the rumor,a spreader will become anR1 sti fler with probabilityδ.

    From the above description,it can be seen that in our SIR model,both the delay time before implementing immunization to ignorants andR2 sti flers spreading the truth of rumors to spreaders are taken into consideration.Obviously,our SIR model that is great different from the original models is more realistic.

    3 SIR Model Analysis

    For the homogeneous network,each node degree is approximately equal to the average degree of the network〈k〉.LetS(t),I(t),R1(t)andR2(t)denote the densities of ignorants,spreaders,R1 sti flers andR2 sti flers at timet,respectively.Obviously,these four variables meet the normalization conditionS(t)+I(t)+R1(t)+R2(t)=1.Then,according to the propagation rules of the proposed SIR model,we establish the mean- field equations as follows:

    When a rumor begins spreading on the networks,it is assumed that there is only one node has accepted the rumor.So we can obtain the initial conditions for the above four variables as follows

    Since the existence of delay time,for the propagation timet<T,R2(t)=0.However,whent=T,the initial value ofR2(T)can be get thatR2(T)=f,and at this timeI(T)?f→I(T).

    Considering the initial conditions as in Eq.(5),we can derive the density of ignorants from Eq.(1)as

    De fining an auxiliary function?(t)that is used to represent the value of integration in the exponent of the first term on the right-hand side in Eq.(6)

    Substituting Eq.(7)back into Eq.(6)gives

    When the value ofI(t)is smaller,its higher-order term can be neglected.Then,we can derive the density ofR1 sti flers from Eq.(3)as

    Imposing the initial conditionR2(T)=f,we can solve the differential equation Eq.(4)to obtain that

    By differentiation of?(t),a self-consistent equation about?(t)can be expressed as

    At the steady state of rumor spreading wheret→∞,there are no spreaders left in the networks,i.e.,I(∞)=0.So,we have that

    Assume that the steady state value of?(t)is?∞,and then we can derive the expression of?∞from Eqs.(12)and(13)that

    whereF(?∞)is an auxiliary function.Clearly,?∞=0 is a solution of Eq.(14),which corresponds to the situation where there is no rumor spreading outbreak.In order to have a rumor outbreak,?∞should have a non-zero solution satisfying

    Eq.(15)de fines the critical thresholdλcas

    In Eq.(16),λcobviously increases monotonically withf,and decreases monotonically withg(T).This means that the implementation of random immunization strategy can effectively depress the spread of rumors,but the existence of delay time reduces the immune effect of the immunization strategy.Equation(16)also shows that in the present model,nodes’identification force has no effect on the critical threshold.Considering thatf=α=γ=0,thenλc=1/〈k〉,which is consistent with the classical SIR rumor model.[15]

    When rumor spreading reaches a steady state,We de-

    Whenλ→λc,it is reasonable to neglect the higher-order-term of?∞in Eq.(14).Applying the Maclaurin formula to Eq.(14),we have

    By Eqs.(18)and(19),one can get

    From Eq.(19),we can easily find that,R1(∞)∝f?1andR1(∞)∝g(T).Thus,it can be concluded that both the random immunization strategy and the delay time can bring an important in fluence on the rumor spreading.

    4 Simulations Analysis

    In this section,the propagation dynamical properties of the novel SIR rumor model proposed in this paper are investigated by using sufficient numerical simulations.The Monte Carlo method is adopted to describe the spreading process of rumors.As a more popular homogeneous network,the WS small-world model[29]is used to depict the population.AfterTtime step,thefpercent of nodes that have not contacted rumors are randomly selected as the immunized nodes.The network size isN=5000,the node average degree is〈k〉=6,and the rewiring probability isp=0.1;moreover,δ=1,σ=1,andγ=1.At the initial moment of rumor spreading,a single node is randomly selected as the propagation source.All the results are obtained by averaging each simulation at least 100 runs with different initial spreaders.

    Figure 2 describes the variation of the critical threshold withλcthe immunization proportionf.From Fig.2,one can see that due to the in fluence of delay time,whenf=0,λc<1〈k〉of the classical SIR model on the homogeneous networks.[15]Figure 2 also shows that as the value offincreases,λcobviously increases.Figure 3 illustrates the variation of the value ofR1(∞)with the effective propagation rate.From this figure,we can see that when the rumor propagation comes to a steady state,the number of nodes that finally accept the rumor sharply decreases with the value offincreases.Thus,combining Figs.2 and 3,it can be inferred that even if considering the existence of the delay time,the random immunization strategy is still effective for preventing rumor spreading on the homogeneous networks,which also proves the correctness of the theory analysis in Sec.3.

    Fig.2 The relationship between the critical threshold λcand the immunization percentage f.The parameters are T=1 and α=0.1.

    Fig.3 The relationship between the steady state value of R1 sti flers R1(∞)and the effective propagation rate λ when the value of f varies.The parameters are T=2 and α=0.1.

    Figure 4 depicts the critical thresholdλcvaries with the delay timeT.From Fig.4,we find thatλcdecreases slowly with the increase ofT,which is consistent with the theory analysis in Sec.3.Compared with the larger value ofT,the smaller value ofTleads to more obviously decrease ofλc.Figure 5 shows the steady state value ofR1 sti flersR1(∞)depends on the delay timeT.From this figure one can see thatR1(∞)clearly increases as the value ofTincreases.From Figs.4 and 5,it can be followed that the sooner the immunization measure is implemented,the better the immune effect will be.Therefore,whether we can find rumors spreading on the network as soon as possible is essential for the control of rumor propagation.

    Fig.4 The relationship between the critical threshold λcand the delay time T.The parameters are f=0.05 and α=0.5.

    Fig.5 The relationship between the steady state value of R1 sti flers R1(∞)and the the effective propagation rate λ when the value of T varies.The parameters are f=0.02 and α=0.1.

    Fig.6 The relationship between the steady state value of R1 sti flers R1(∞)and the effective propagation rate λ when the value of α varies.The parameters are T=3 and f=0.1.

    Figures 6 and 7 depict the relationship between the values ofR1(∞),R2(∞)and the critical thresholdλcwith the value ofαvarying.From these two figures,we can find that for a given value ofλ,as the value ofαincreases,the value ofR1(∞)evidently decreases,but the value ofR1(∞)distinctly increases.This implies that the stronger the reliability of the truth of rumors,the more spreaders becomeR2 sti flers,which accordingly reduces the number of nodes that finally accept the rumor.Thus,in order to better control the rumor spreading,the truth of rumors should be published by the more authoritative department,which helps to enhance the reliability of the truth of rumors accordingly.

    Fig.7 The relationship between the steady state value of R2 sti flers R2(∞)and the effective propagation rate λ when the value of α varies.The parameters are T=3 and f=0.1.

    Figure 8 shows the relationship between the steady state value ofR1 sti flersR1(∞)and the parameterγ.From this figure we know that,for the given value ofλ,the value ofR1(∞)decreases slowly as the value ofγincreases.This is because that the stronger the identification force of ignorants,the less the number of spreaders,so that the value ofR1(∞)is decreased.Therefore,the propagation degree of rumors can be alleviated by enhancing the identification force of ignorants.Moreover,agreeably to theoretical analysis in Sec.3,we also find from the figure that the parameterγdoes not change the critical thresholdλc.

    Fig.8 The relationship between the steady state value of R1 sti flers R1(∞)and the effective propagation rate λ when the value of γ varies.The parameters are T=3 and f=0.1.

    Figure 9 gives the relationship between the density ofR1 sti flersR1(t)and the spreading timet.It has been seen that as the timetincreases,R1(t)increases exponentially.After some time the rumor spreading comes to a steady state which will remain constant,since there are not any more spreaders in the network at that time.It has also been observed that the larger the value off,the slower the spread of the rumor,and the less the number of nodes that accept the rumor.The density of spreadersI(t)is plotted against the propagation timetin Fig.10.It has observed thatI(t)increases exponentially with the timet,but after achieving a maximum it decays exponentially.Figure 10 also shows that as the value offincreases,the maximum ofI(t)decreases,but the time of rumor spreading is prolonged,which is conductive to taking measures to prevent and control the spread of rumors.

    Fig.9 The relationship between the density of R1 stiflers R1(t)and the time t when the value of f varies.The parameters are T=5 and α=0.1.

    Fig.10 The relationship between the density of ignorants I(t)and the time t when the value of f varies.The parameters are T=5 and α=0.1.

    In Fig.11,the density ofR1 sti flersR1(t)has been plotted against the transmission timet.One can clearly observe that when the value oftis small(e.g.,t<10),the values ofR1(t)are almost the same for different values ofα.However,when the value oftis large,R1(t)apparently decreases with the increase ofα.The main reason is that as the reliability of the truth increases,more and more spreaders becomeR2 sti flers,as a result abating the propagation degree of rumors.

    Fig.11 The relationship between the density of R1 stiflers R1(t)and the time t when the value of α varies.The parameters are T=6 and f=0.05.

    Fig.12 The relationship between the density of ignorants I(t)and the time t when the value of α varies.The parameters are T=6 and f=0.05.

    Figures 12 and 13 illustrate the general trends for the density of spreadersI(t)over the spreading timetwith the values ofαandTvarying,respectively.Figure 12 shows that in the process of rumor spreading,as the value ofαincreases,the maximum number of spreaders slightly decreases.That is the propagation of the truth making part of spreaders intoR2 sti flers.Similar to the immune mechanism,the spread of the truth can also inhibit to some extent the spread of rumors.Figure 13 shows that the larger the value ofT,the greater the number of spreaders,and the longer the spread of rumors.Therefore,in order to better prevent and control the spread of rumors,we should not only enhance the reliability of the truth as much as possible,but also immunize the network as early as possible.

    Fig.13 The relationship between the density of ignorants I(t)and the time t when the value of T varies.The parameters are α=0.1 and f=0.05.

    5 Conclusions

    The implementation of immunization strategy for the networks is an important way to prevent the spread of rumors.In this paper,considering the in fluence of delay time and the spread of truth,we have constructed a novel SIR rumor spreading model to investigate the effect of random immunization strategy on homogeneous networks.We found that the existence of delay time reduces the effect of immunization strategy,but the spread of truth can decrease the propagation degree of rumors on the networks.Therefore,it is very important to detect rumor spreading on the networks timely and publish the truth by the authoritative department.Moreover,we also found that in consideration of the effect of delay time,the network nodes’identification force can still exert an influence on the propagation behaviors of rumors,which is consistent with previous research conclusions.

    The results obtained in the course of our study considered the case where each immune node has the same delay time.In reality,the time that each person contacts the truth of rumors is different,i.e.,there is a difference among the delay time of each person.Thus,it is very interesting to investigate the impact of the difference among each person’s delay time on the spread of rumors.In the future,we will focus on this research.

    [1]R.Bhavnani,M.G.Findley,and J.H.Kuklinski,J.Politics 71(2009)876.

    [2]C.R.Sunstein and A.Vermeule,J.Political Philos.17(2009)202.

    [3]M.Del.Vicario,A.Bessi,and F.Zollo,Proc.Natl.Acad.Sci.U.S.A.113(2016)554.

    [4]Y.Liu,S.M.Diao,and Y.X.Zhu,Physica A 461(2016)543.

    [5]M.Kosfeld,J.Math.Econ.41(2005)646.

    [6]S.A.Thomas,Sociological Spectrum 27(2007)679.

    [7]Z.Zhang and Z.Zhang,Physica A 388(2009)4159.

    [8]D.J.Daley and D.G.Kendall,IMA J.Appl.Math.1(1965)42.

    [9]A.Sudbury,Journal of Applied Probability 22(1985)443.

    [10]D.H.Zanette,Phys.Rev.E 65(2002)041908.

    [11]R.Pastor-Satorras and A.Vespignani,Phys.Rev.Lett.86(2001)3200.

    [12]C.Castellano and R.Pastor-Satorras,Phys.Rev.Lett.105(2010)218701.

    [13]R.Yang,B.H.Wang,and J.Ren,Phys.Lett.A 364(2007)189.

    [14]Y.Moreno,M.Nekovee,and A.F.Pacheco,Phys.Rev.E 69(2004)066130.

    [15]M.Nekovee,Y.Moreno,and G.Bianconi,Physica A 374(2007)457.

    [16]Y.Moreno,M.Nekovee,and A.Vespignani,Phys.Rev.E 69(2004)055101.

    [17]D.Li and J.Ma,Physica A 469(2017)284.

    [18]G.Cs′anyi and B.Szendroi,Phys.Rev.E 69(2004)036131.

    [19]H.Ebel,L.I.Mielsch,and S.Bornholdt,Phys.Rev.E 66(2002)035103.

    [20]L.Zhao,H.Cui,and X.Qiu,Physica A 392(2013)995.

    [21]L.Zhao,Q.Wang,and J.Cheng,Physica A 390(2011)2619.

    [22]X.Zhao and J.Wang,Discrete Dyn.Nat.Soc.2013(2013)1.

    [23]S.Han,F.Zhuang,and Q.He,Physica A 394(2014)99.

    [24]N.Madar,T.Kalisky,and R.Cohen,The European Physical Journal b-Condensed Matter and Complex Systems 38(2004)269.

    [25]J.Huang and X.Jin,Journal of Systems Science and Complexity 24(2011)449.

    [26]L.Sun,Y.Liu,and Q.A.Zeng,Int.J.Mod.Phys.C 26(2015)1550080.

    [27]Z.He,Z.Cai,and J.Yu,IEEE Trans.Veh.Technol.99(2017)1.

    [28]L.Zhao,J.Wang,and R.Huang,PloS One 10(2015)e0124978.

    [29]D.J.Watts and S.H.Strogatz,Nature(London)393(1998)440.

    猜你喜歡
    王靜李敏
    Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schr¨odinger equation
    The Management Methods And Thinking Of Personnel Files
    客聯(lián)(2021年9期)2021-11-07 19:21:33
    The Development of Contemporary Oil Painting Art
    青年生活(2019年16期)2019-10-21 01:46:49
    王靜博士簡介
    Income Inequality in Developing Countries
    商情(2017年17期)2017-06-10 12:27:58
    Let it Go隨它吧
    RIGIDITY OF COMPACT SURFACES IN HOMOGENEOUS 3-MANIFOLDS WITH CONSTANT MEAN CURVATURE?
    Discussion on James Joyce’s The Dead
    西江文藝(2016年6期)2016-05-30 23:28:20
    The Influence of Missionary School on China’s Foreign LanguageEducation
    西江文藝(2016年6期)2016-05-30 07:53:17
    張碧晨 演繹新一代GIRL POWER
    Coco薇(2016年4期)2016-04-06 16:57:38
    老熟妇仑乱视频hdxx| 国产av又大| 国产成人欧美在线观看 | 亚洲avbb在线观看| 五月天丁香电影| 乱人伦中国视频| 美女高潮喷水抽搐中文字幕| 国产黄色免费在线视频| 久久午夜综合久久蜜桃| 亚洲精品第二区| 国产精品影院久久| 成人免费观看视频高清| 亚洲国产av影院在线观看| 窝窝影院91人妻| 一边摸一边做爽爽视频免费| 欧美黄色片欧美黄色片| 亚洲美女黄色视频免费看| 多毛熟女@视频| 亚洲精品国产av成人精品| 亚洲精品一区蜜桃| 黄色视频,在线免费观看| 免费在线观看黄色视频的| 久久人人爽av亚洲精品天堂| 亚洲精品中文字幕在线视频| 国产三级黄色录像| 午夜老司机福利片| 亚洲欧美一区二区三区久久| 91字幕亚洲| 久久久久精品人妻al黑| 国产成人av教育| 日日夜夜操网爽| 老司机靠b影院| 美女高潮喷水抽搐中文字幕| 中文欧美无线码| 久久午夜综合久久蜜桃| 国产视频一区二区在线看| 人妻 亚洲 视频| 天天操日日干夜夜撸| av又黄又爽大尺度在线免费看| 国产在视频线精品| 国产淫语在线视频| 又大又爽又粗| 高潮久久久久久久久久久不卡| 亚洲成人免费电影在线观看| 99国产精品免费福利视频| 欧美亚洲 丝袜 人妻 在线| av一本久久久久| 日韩 亚洲 欧美在线| 成年动漫av网址| 啪啪无遮挡十八禁网站| 人人澡人人妻人| 国产精品一二三区在线看| 国产精品国产av在线观看| 久久久久久久久久久久大奶| 久久综合国产亚洲精品| 性色av一级| 极品少妇高潮喷水抽搐| 亚洲成人国产一区在线观看| 亚洲精华国产精华精| 亚洲美女黄色视频免费看| 午夜免费鲁丝| 久久人人97超碰香蕉20202| 美女高潮到喷水免费观看| 久久精品久久久久久噜噜老黄| 啦啦啦中文免费视频观看日本| 欧美日韩亚洲高清精品| 国产有黄有色有爽视频| 午夜久久久在线观看| 亚洲欧美精品综合一区二区三区| 美女高潮喷水抽搐中文字幕| 精品一区二区三区四区五区乱码| 亚洲欧美一区二区三区久久| 亚洲国产看品久久| 欧美日韩成人在线一区二区| 看免费av毛片| 久久精品国产a三级三级三级| 午夜福利免费观看在线| 成人三级做爰电影| 国产精品国产三级国产专区5o| 深夜精品福利| 久久久精品国产亚洲av高清涩受| 亚洲自偷自拍图片 自拍| 波多野结衣av一区二区av| 国产伦人伦偷精品视频| 欧美精品av麻豆av| 久久久久久人人人人人| 国产有黄有色有爽视频| 久久久久精品国产欧美久久久 | 久久人妻熟女aⅴ| 大码成人一级视频| 韩国高清视频一区二区三区| 视频区欧美日本亚洲| 日本wwww免费看| 咕卡用的链子| tube8黄色片| 亚洲av日韩在线播放| www.精华液| 亚洲欧美日韩另类电影网站| 亚洲人成电影观看| 两个人看的免费小视频| 精品人妻1区二区| 中文字幕人妻丝袜制服| 亚洲avbb在线观看| 悠悠久久av| 国产精品.久久久| 一区在线观看完整版| 中文字幕av电影在线播放| 乱人伦中国视频| 免费女性裸体啪啪无遮挡网站| 一级片'在线观看视频| 国产精品1区2区在线观看. | 日韩制服丝袜自拍偷拍| 天天操日日干夜夜撸| 国产亚洲午夜精品一区二区久久| 婷婷成人精品国产| 免费观看人在逋| 亚洲国产中文字幕在线视频| 12—13女人毛片做爰片一| 一个人免费在线观看的高清视频 | 男人舔女人的私密视频| 国产一区二区三区在线臀色熟女 | 国产91精品成人一区二区三区 | 久久国产亚洲av麻豆专区| 精品亚洲成a人片在线观看| 天堂中文最新版在线下载| 久久久国产一区二区| 国产视频一区二区在线看| 捣出白浆h1v1| 欧美一级毛片孕妇| 999久久久精品免费观看国产| 黄色视频不卡| 在线av久久热| 亚洲三区欧美一区| 亚洲性夜色夜夜综合| 91麻豆av在线| 久久久久久久大尺度免费视频| 亚洲性夜色夜夜综合| 欧美日韩亚洲国产一区二区在线观看 | 男女下面插进去视频免费观看| 男女高潮啪啪啪动态图| 手机成人av网站| 日韩视频在线欧美| 国产精品二区激情视频| av电影中文网址| 老司机在亚洲福利影院| 97在线人人人人妻| 免费在线观看完整版高清| 亚洲欧美一区二区三区黑人| 亚洲国产av新网站| 国产精品 欧美亚洲| 精品国产乱子伦一区二区三区 | 免费在线观看完整版高清| 久久亚洲国产成人精品v| 日韩,欧美,国产一区二区三区| 国产成人精品久久二区二区91| 黄片大片在线免费观看| 亚洲精品国产一区二区精华液| 国产成人精品久久二区二区免费| www.自偷自拍.com| 日韩,欧美,国产一区二区三区| 精品福利永久在线观看| av片东京热男人的天堂| 日日摸夜夜添夜夜添小说| 欧美成人午夜精品| 日韩欧美一区视频在线观看| 亚洲男人天堂网一区| 国产三级黄色录像| 桃红色精品国产亚洲av| 亚洲精品久久午夜乱码| 国产日韩欧美视频二区| 国产亚洲一区二区精品| 女人高潮潮喷娇喘18禁视频| 国产主播在线观看一区二区| 蜜桃在线观看..| 国产福利在线免费观看视频| 亚洲精华国产精华精| 国产精品一区二区在线不卡| 午夜91福利影院| 老熟妇仑乱视频hdxx| 国产xxxxx性猛交| 欧美xxⅹ黑人| 男人操女人黄网站| 久久ye,这里只有精品| 狂野欧美激情性bbbbbb| 国产日韩欧美在线精品| 欧美日韩亚洲综合一区二区三区_| 一区在线观看完整版| 国产片内射在线| 日韩 亚洲 欧美在线| 亚洲av男天堂| 亚洲精品中文字幕一二三四区 | 成年人黄色毛片网站| 国产麻豆69| 熟女少妇亚洲综合色aaa.| 午夜免费鲁丝| 男人舔女人的私密视频| 99re6热这里在线精品视频| 亚洲五月婷婷丁香| 午夜激情久久久久久久| 两性午夜刺激爽爽歪歪视频在线观看 | 大片免费播放器 马上看| 亚洲精品国产区一区二| 国产精品久久久人人做人人爽| 国产精品一区二区在线观看99| 一区二区三区精品91| 高清在线国产一区| 五月天丁香电影| 午夜福利视频在线观看免费| 国产一区二区激情短视频 | 亚洲精品中文字幕在线视频| 久久亚洲国产成人精品v| 色精品久久人妻99蜜桃| 大片电影免费在线观看免费| 一本久久精品| 精品亚洲乱码少妇综合久久| 国产一区二区激情短视频 | 亚洲精品中文字幕在线视频| 亚洲精品美女久久av网站| 免费人妻精品一区二区三区视频| 欧美性长视频在线观看| 国产成人精品在线电影| 人人妻人人添人人爽欧美一区卜| 考比视频在线观看| 夜夜夜夜夜久久久久| 丰满饥渴人妻一区二区三| 久久人妻福利社区极品人妻图片| 两个人看的免费小视频| 欧美变态另类bdsm刘玥| 久久久久国产一级毛片高清牌| 999久久久精品免费观看国产| 精品免费久久久久久久清纯 | 一级毛片电影观看| 巨乳人妻的诱惑在线观看| 欧美日韩一级在线毛片| 国产精品久久久久久精品电影小说| 日韩三级视频一区二区三区| av天堂久久9| 国产野战对白在线观看| 国产成人一区二区三区免费视频网站| 性色av一级| 亚洲国产精品一区二区三区在线| 亚洲av片天天在线观看| 十八禁网站网址无遮挡| 国产片内射在线| 精品亚洲成国产av| 男人操女人黄网站| 精品福利观看| 满18在线观看网站| 中文字幕精品免费在线观看视频| 精品久久久久久久毛片微露脸 | 精品国产一区二区三区四区第35| 亚洲免费av在线视频| 婷婷成人精品国产| 免费人妻精品一区二区三区视频| 老司机影院成人| 欧美日韩中文字幕国产精品一区二区三区 | 在线av久久热| 乱人伦中国视频| 欧美精品一区二区免费开放| 午夜激情av网站| 91精品三级在线观看| 国产激情久久老熟女| av天堂在线播放| 国产一区二区三区av在线| 欧美激情久久久久久爽电影 | 国产97色在线日韩免费| 老熟女久久久| 99精品久久久久人妻精品| 97精品久久久久久久久久精品| 日韩欧美免费精品| 国产成人精品久久二区二区免费| 国产一区二区激情短视频 | 成在线人永久免费视频| 精品少妇内射三级| 黄色视频不卡| 一级毛片女人18水好多| 亚洲,欧美精品.| 777米奇影视久久| 在线亚洲精品国产二区图片欧美| 18在线观看网站| 99国产精品一区二区三区| 国产免费现黄频在线看| 亚洲色图综合在线观看| 十八禁网站免费在线| √禁漫天堂资源中文www| 亚洲精品一区蜜桃| 别揉我奶头~嗯~啊~动态视频 | 菩萨蛮人人尽说江南好唐韦庄| 亚洲精品中文字幕在线视频| 国产精品成人在线| 国产日韩欧美视频二区| 18在线观看网站| 丝袜脚勾引网站| 精品国产一区二区三区久久久樱花| xxxhd国产人妻xxx| 人妻一区二区av| 可以免费在线观看a视频的电影网站| 少妇粗大呻吟视频| 69精品国产乱码久久久| 亚洲国产欧美日韩在线播放| 波多野结衣一区麻豆| 麻豆乱淫一区二区| 免费看十八禁软件| 色老头精品视频在线观看| 国产一区二区三区在线臀色熟女 | 亚洲七黄色美女视频| 91精品伊人久久大香线蕉| www.999成人在线观看| 国产人伦9x9x在线观看| kizo精华| av天堂久久9| 久热这里只有精品99| 91麻豆av在线| 青春草视频在线免费观看| 最新在线观看一区二区三区| 亚洲精品一区蜜桃| 99热网站在线观看| 在线观看人妻少妇| 两人在一起打扑克的视频| 成年av动漫网址| 久久久国产成人免费| 亚洲中文字幕日韩| 成年人黄色毛片网站| 日韩 亚洲 欧美在线| 国产一区二区激情短视频 | 亚洲国产毛片av蜜桃av| 母亲3免费完整高清在线观看| 美国免费a级毛片| 久久精品人人爽人人爽视色| 丝袜美足系列| 国产免费现黄频在线看| netflix在线观看网站| 性高湖久久久久久久久免费观看| 日日摸夜夜添夜夜添小说| 久久亚洲国产成人精品v| 成人国语在线视频| 又黄又粗又硬又大视频| 在线永久观看黄色视频| 欧美日韩成人在线一区二区| 99久久99久久久精品蜜桃| 久热这里只有精品99| 自拍欧美九色日韩亚洲蝌蚪91| 亚洲少妇的诱惑av| 18禁裸乳无遮挡动漫免费视频| av线在线观看网站| 女人精品久久久久毛片| 国产在线观看jvid| 大片电影免费在线观看免费| 一区二区日韩欧美中文字幕| 黑人猛操日本美女一级片| 精品国产一区二区三区四区第35| 亚洲国产中文字幕在线视频| 国产精品久久久人人做人人爽| 国产成人系列免费观看| 可以免费在线观看a视频的电影网站| 国产亚洲av片在线观看秒播厂| 三级毛片av免费| 在线亚洲精品国产二区图片欧美| 18禁黄网站禁片午夜丰满| 在线亚洲精品国产二区图片欧美| 亚洲欧美成人综合另类久久久| 久久久久久久大尺度免费视频| 69精品国产乱码久久久| www.自偷自拍.com| 久久久久久亚洲精品国产蜜桃av| 波多野结衣av一区二区av| 成人国语在线视频| 亚洲国产看品久久| 欧美中文综合在线视频| 久久久欧美国产精品| 正在播放国产对白刺激| 亚洲成av片中文字幕在线观看| 天堂8中文在线网| 欧美黑人欧美精品刺激| 一级毛片精品| 岛国毛片在线播放| 国产免费一区二区三区四区乱码| 亚洲av电影在线进入| 精品卡一卡二卡四卡免费| 天天添夜夜摸| 热99国产精品久久久久久7| 在线看a的网站| 女性被躁到高潮视频| 永久免费av网站大全| 欧美日韩av久久| av超薄肉色丝袜交足视频| 一级a爱视频在线免费观看| 久久免费观看电影| 激情视频va一区二区三区| tocl精华| 亚洲av成人不卡在线观看播放网 | 久久精品国产a三级三级三级| 亚洲伊人久久精品综合| 亚洲第一av免费看| 亚洲综合色网址| 精品一区二区三卡| 国产高清videossex| 久久中文看片网| 亚洲国产精品一区三区| 亚洲久久久国产精品| 亚洲色图综合在线观看| 天天添夜夜摸| 久久久久网色| 桃红色精品国产亚洲av| 纯流量卡能插随身wifi吗| 黄色片一级片一级黄色片| 精品亚洲乱码少妇综合久久| 精品欧美一区二区三区在线| 国产免费av片在线观看野外av| 国产精品一区二区在线不卡| 亚洲国产日韩一区二区| 99久久综合免费| 香蕉丝袜av| 色老头精品视频在线观看| 色精品久久人妻99蜜桃| 美女视频免费永久观看网站| 亚洲欧美成人综合另类久久久| 国产日韩欧美亚洲二区| av网站在线播放免费| 美女午夜性视频免费| √禁漫天堂资源中文www| 18禁国产床啪视频网站| 久久 成人 亚洲| 黄色视频,在线免费观看| 久久精品亚洲熟妇少妇任你| 亚洲一区二区三区欧美精品| 国产精品久久久久久精品古装| 18禁黄网站禁片午夜丰满| 涩涩av久久男人的天堂| 国产亚洲午夜精品一区二区久久| 欧美黑人欧美精品刺激| 国产免费一区二区三区四区乱码| 国产成人精品久久二区二区91| 亚洲精品一卡2卡三卡4卡5卡 | 777久久人妻少妇嫩草av网站| 欧美亚洲 丝袜 人妻 在线| 老汉色∧v一级毛片| 国产成人一区二区三区免费视频网站| 国产日韩欧美在线精品| 欧美大码av| 19禁男女啪啪无遮挡网站| 欧美日韩国产mv在线观看视频| 国产免费福利视频在线观看| 97精品久久久久久久久久精品| 欧美精品一区二区免费开放| 亚洲精品一区蜜桃| 免费久久久久久久精品成人欧美视频| 99精品欧美一区二区三区四区| 啦啦啦在线免费观看视频4| 99国产综合亚洲精品| www日本在线高清视频| 男女免费视频国产| 黄网站色视频无遮挡免费观看| 久久精品亚洲av国产电影网| 久久久精品区二区三区| 一进一出抽搐动态| 欧美97在线视频| 久久久久精品国产欧美久久久 | 欧美大码av| 岛国毛片在线播放| 亚洲va日本ⅴa欧美va伊人久久 | 亚洲一区中文字幕在线| 在线观看免费日韩欧美大片| 国产在线一区二区三区精| 老司机午夜福利在线观看视频 | 亚洲av日韩精品久久久久久密| 人妻人人澡人人爽人人| 视频在线观看一区二区三区| 每晚都被弄得嗷嗷叫到高潮| 最新在线观看一区二区三区| 国产又色又爽无遮挡免| 91精品伊人久久大香线蕉| 国产免费福利视频在线观看| 在线观看www视频免费| 99热国产这里只有精品6| 国产一区有黄有色的免费视频| 国产片内射在线| www.av在线官网国产| 国产精品久久久久成人av| 亚洲av国产av综合av卡| 黑人巨大精品欧美一区二区蜜桃| 熟女少妇亚洲综合色aaa.| 日本精品一区二区三区蜜桃| 精品卡一卡二卡四卡免费| 精品福利永久在线观看| 女人被躁到高潮嗷嗷叫费观| 久久久久国产一级毛片高清牌| 宅男免费午夜| netflix在线观看网站| av网站免费在线观看视频| 超碰97精品在线观看| av片东京热男人的天堂| 午夜福利一区二区在线看| 一区二区三区四区激情视频| 亚洲av日韩在线播放| 另类精品久久| 亚洲免费av在线视频| 国产精品国产av在线观看| 国产1区2区3区精品| 欧美xxⅹ黑人| 超碰97精品在线观看| 性少妇av在线| 国产免费av片在线观看野外av| 黄色毛片三级朝国网站| 99国产精品一区二区蜜桃av | 久热爱精品视频在线9| 久久久国产成人免费| 在线观看一区二区三区激情| 黄色a级毛片大全视频| 精品国产乱码久久久久久男人| 国产视频一区二区在线看| 国产精品秋霞免费鲁丝片| 日韩欧美一区视频在线观看| 少妇猛男粗大的猛烈进出视频| 大型av网站在线播放| 丝袜在线中文字幕| 成年女人毛片免费观看观看9 | 午夜视频精品福利| 2018国产大陆天天弄谢| 国产欧美日韩精品亚洲av| 无限看片的www在线观看| 在线观看免费日韩欧美大片| 丝袜喷水一区| 50天的宝宝边吃奶边哭怎么回事| 叶爱在线成人免费视频播放| 性色av一级| 首页视频小说图片口味搜索| 99精品欧美一区二区三区四区| 亚洲专区字幕在线| 成年人黄色毛片网站| 亚洲欧美色中文字幕在线| 久久久久久久久免费视频了| 久久人妻熟女aⅴ| 久久久精品区二区三区| 狂野欧美激情性xxxx| 深夜精品福利| 女性被躁到高潮视频| 美女主播在线视频| 男人添女人高潮全过程视频| 淫妇啪啪啪对白视频 | 精品卡一卡二卡四卡免费| 亚洲一区二区三区欧美精品| 极品少妇高潮喷水抽搐| 黑人欧美特级aaaaaa片| 香蕉丝袜av| 欧美日韩黄片免| 亚洲免费av在线视频| 亚洲国产精品999| 无限看片的www在线观看| 国产一区二区三区av在线| 日本欧美视频一区| 亚洲 欧美一区二区三区| 精品福利永久在线观看| 国产深夜福利视频在线观看| 中文字幕最新亚洲高清| 黄色视频,在线免费观看| 国产亚洲一区二区精品| 国产成人欧美在线观看 | 免费黄频网站在线观看国产| 国产日韩一区二区三区精品不卡| 黄频高清免费视频| 悠悠久久av| 亚洲欧洲日产国产| 久久女婷五月综合色啪小说| 亚洲中文字幕日韩| 亚洲国产欧美在线一区| av有码第一页| 亚洲欧美精品综合一区二区三区| 69精品国产乱码久久久| 精品视频人人做人人爽| 男男h啪啪无遮挡| 汤姆久久久久久久影院中文字幕| 天天躁狠狠躁夜夜躁狠狠躁| av网站在线播放免费| videosex国产| 国产亚洲av高清不卡| 中出人妻视频一区二区| 免费高清视频大片| 老熟妇乱子伦视频在线观看| 99久久国产精品久久久| 亚洲,欧美精品.| 欧美日韩瑟瑟在线播放| 无人区码免费观看不卡| 黄片小视频在线播放| 特级一级黄色大片| 中国美女看黄片| 999精品在线视频| √禁漫天堂资源中文www| 欧美性猛交╳xxx乱大交人| 欧美日韩黄片免| 日韩欧美在线二视频| 国产精品av久久久久免费| 麻豆久久精品国产亚洲av| 亚洲国产精品久久男人天堂| 久久人妻福利社区极品人妻图片| 少妇粗大呻吟视频| 国内久久婷婷六月综合欲色啪| 叶爱在线成人免费视频播放| 免费在线观看影片大全网站| 日本在线视频免费播放| 少妇裸体淫交视频免费看高清 | 久久久久国内视频| 美女大奶头视频| 中文字幕高清在线视频| 成人手机av| 美女大奶头视频| 麻豆一二三区av精品| 男插女下体视频免费在线播放| 国产不卡一卡二| 亚洲av片天天在线观看| 后天国语完整版免费观看| 久久99热这里只有精品18| 好看av亚洲va欧美ⅴa在| 好男人在线观看高清免费视频| 黄色女人牲交|