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In this paper, we establish a susceptible-infected-removed (SIR) rumor spreading model based on the influence of rumor-refuting mechanism and time delay on internet rumor spreading. The threshold R0 of rumor spreading is obtained by using the spectral radius method of regenerative matrix; the conditions for the existence of rumor prevailing equilibrium point are given according to the quadratic function characteristics; the local stability of rumor-free equilibrium point and rumor prevailing equilibrium point are established by using eigenvalue theory and Routh-Hurwitz criterion; and the criterion for the occurrence of Hopf bifurcation is also established. The numerical simulation results show that the information about refuting rumors, released by the government and the media, can accelerate the convergence rate of rumors and reduce the maximum density of rumor-spreaders.
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Keywords:
- rumor propagation /
- time delay /
- rejection mechanism /
- Hopf bifurcation
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图 1
$\alpha$ 对辟谣函数$h\left(I\right)= {rI}/({1+\alpha I})$ 的影响Fig. 1. The influence of α on the rejection mechanism
$h\left(I\right)= {rI}/({1+\alpha I})$ .
图 3 (a)
${ R}_{0} < 1$ ; (b)${ R}_{0} > 1$ Fig. 3. (a)
${ R}_{0} < 1$ ; (b)${ R}_{0} > 1$ .
图 4 (a)
${R}_{0} < 1$ ; (b)${R}_{0} > 1$ Fig. 4. (a)
${R}_{0} < 1$ ; (b)${R}_{0} > 1$ .
图 5 出生率
$\varLambda$ 与恢复率r对基本再生数$ {R}_{0}$ 的影响Fig. 5. Influence of birth rate
$\varLambda$ and recover rate r on the basic productive number${R}_{0}$ . -
[1] Zhu L H, Zhao H Y, Wang H Y 2019 Phys. Scr. 94 085007
Google Scholar
[2] Zhao L J, Wang Q, Cheng J J, Chen Y C, Wang J J, Huang W 2011 Physica A 390 2619
Google Scholar
[3] 顾亦然, 夏玲玲 2012 物理学报 61 238701
Google Scholar
Gu Y R, Xia L L 2012 Acta Phys. Sin. 61 238701
Google Scholar
[4] 王辉, 韩江洪, 邓林, 程克勤 2013 物理学报 62 110505
Google Scholar
Wang H, Han J H, Deng L, Cheng K Q 2013 Acta Phys. Sin. 62 110505
Google Scholar
[5] 赵洪涌, 朱霖河 2015 南京航空航天大学学报 47 332
Zhao H Y, Zhu L H 2015 J. Nanjing University of Aeronautics & Astronautics 47 332
[6] Liu Q, Chen Q M, Jiang D Q 2016 Physica A 450 115
Google Scholar
[7] Ma K, Li W H, Guo Q T, Zheng X Q, Zheng Z M, Gao C, Tang S T 2018 Physica A 492 21
Google Scholar
[8] 吴晓, 刘万平, 杨武, 卢玲, 刘小洋, 黄诗雯 2018 复杂系统与复杂性科学 15 34
Wu X, Liu W P, Yang W, Lu L, Liu X Y, Huang S W 2018 J. Complex Syst. Complexity Sci. 15 34
[9] 王飞雪, 李芳 2019 计算机应用研究 36 1
Wang F X, LI F 2019 J. Appl. Res. Comput. 36 1
[10] 张菊平, 郭昊明, 荆文君, 靳祯 2019 物理学报 68 150501
Google Scholar
Zhang J P, Guo H M, Jing W J, Jin Z 2019 Acta Phys. Sin. 68 150501
Google Scholar
[11] Hu Y H, Pan Q H, Hou W B, He M F 2018 Physica A 502 331
Google Scholar
[12] Chen N, Zhu X Z, Chen Y Y 2019 Physica A 523 671
Google Scholar
[13] Ma J, Li D D, Tian Z H 2016 Physica A 447 108
Google Scholar
[14] 万贻平, 张东戈, 任清辉 2015 物理学报 64 240501
Google Scholar
Wan Y P, Zhang D G, Ren Q H 2015 Acta Phys. Sin. 64 240501
Google Scholar
[15] Zhang Z K, Liu C, Zhan X X, LU X, Zhang C X, Zhang Y C 2016 Phys. Rep. 651 1
Google Scholar
[16] Jia P Q, Wang C, Zhang G Y, Ma J F 2019 Physica A 524 342
Google Scholar
[17] Zhang R, Wang Y, Zhang Z D, Bi Q S 2015 Nonlinear. Dyn. 79 465
Google Scholar
[18] Miao P, Zhang Z D, Lim C W, Wang X D 2018 Math. Prob. Eng. 2018 6052503
[19] 李旭, 张正娣, 毕勤胜 2013 物理学报 62 220502
Google Scholar
Li X, Zhang Z D, Bi Q S 2013 Acta Phys. Sin. 62 220502
Google Scholar
[20] 邢雅清, 陈小可, 张正娣, 毕勤胜 2016 物理学报 65 090501
Google Scholar
Xing Y Q, Chen X K, Zhang Z D, Bi Q S 2016 Acta Phys. Sin. 65 090501
Google Scholar
[21] 冉茂洁, 刘超, 黄贤英, 刘小洋, 杨宏雨, 张光建 2018 计算机应用 38 3312
Google Scholar
Ran M J, Liu C, Huang X Y, Liu X Y, Yang H Y, Zhang G J 2018 J. Comput. Appl. 38 3312
Google Scholar
[22] 王筱莉, 赵来军, 吴忠 2015 系统工程 33 139
Wang X L, Zhao L J, Wu Z 2015 J. Syst. Eng. 33 139
[23] Askarizadeh M, Ladani B T, Manshaei M H 2019 Physica A 523 21
Google Scholar
[24] Capasso V, Serio G 1978 Math. Biosci. 42 43
Google Scholar
[25] Zhu L H, Guan G, Li Y M 2019 Appl. Math. Model. 70 512
Google Scholar
[26] Huo L A, Wang L, Song G X 2017 Physica A 482 757
Google Scholar
[27] Wang J, Wang Y Q, Li M 2017 Commun. Theor. Phys. 68 803
Google Scholar
[28] Zhu L H, Guan G 2019 Physica A 533 121953
Google Scholar
[29] Laarabi H, Abta A, Rachik M, Bouyaghroumni J 2016 Differ. Equ. Dyn. Syst. 24 407
Google Scholar
[30] Driessche P, Watmough J 2002 Math. Biosci. 180 29
Google Scholar
[31] Al-Darabsah I, Yuan Y 2016 Appl. Math. Comput. 290 307
[32] Zhu L H, Zhao H Y, Wang H Y 2019 Chaos 29 053106
Google Scholar
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