A mathematical model described the propagation of information including rumor and truth presented and its properties investigated. We explored exists of the equilibria, local stability and global asymptotical stability, and obtained the propagation threshold of rumor spreading. Numerical simulation is shown to demonstrate our results. Uncertainty and sensitivity analysis shows the importance of the parameters in our model.
Zhu, H. (2010) Psychological Impact of Rumors of Public Health Emergencies on Hainan People. Medicine & Society, 23, 15-17.
Steele, T.J., Smith, S.M. and Mcbroom, W.H. (1999) Consumer Rumors and Corporate Communications: Rumor Etiology, Background, and Potential Devastating Consequences. Journal of Marketing Management, 9, 95-97.
Wakamatsu, H. and Miyata, T. (2014) Impacts of Actual Harm and Harmful Rumors from Radioactive Spill from the Fukushima Disaster on the Japanese Seafood Market. International Institute of Fisheries Economics & Trade.
Kermack, W.O. and Mckendrick, A.G. (1991) Contributions to the Mathematical Theory of Epidemics-I. Bulletin of Mathematical Biology, 53, 89-118.
Li, M.Y., Graef, J.R., Wang, L., et al. (1999) Global Dynamics of a Seir Model with Varying Total Population Size. Mathematical Biosciences, 160, 191-213. https://doi.org/10.1016/S0025-5564(99)00030-9
Li, M.Y. and Muldowney, J.S. (1999) Global Stability for the Seir Model in Epidemiology. Mathematical Biosciences, 125, 155-164. https://doi.org/10.1016/0025-5564(95)92756-5
Wang, N., Pang, J. and Wang, J. (2014) Stability Analysis of a Multigroup Seir Epidemic Model with General Latency Distributions. Abstract & Applied Analysis, 2014, Article ID: 740256. https://doi.org/10.1155/2014/740256
Egbetade, S.A. and Ibrahim, M.O. (2013) Stability Analysis of Equilibrium States of an Seir Tuberculosis Model. Journal of the Nigerian Association of Mathematical Physics, 20, 119-124.
Tipsri, S. and Chinviriyasit, W. (2014) Stability Analysis of Seir Model with Saturated Incidence and Time Delay. IJAPM, 4, 42-45. https://doi.org/10.7763/IJAPM.2014.V4.252
Meng, F., Li, M.Y. and Ke, W. (2001) Global Stability of an Seis Epidemic Model with Recruitment and a Varying Total Population Size. Mathematical Biosciences, 170, 199-208. https://doi.org/10.1016/S0025-5564(00)00067-5
Liu, W.M. and van den Driessche, P. (1995) Epidemiological Models with Varying Population Size and Dose-Dependent Latent Period. Mathematical Biosciences, 128, 57-69. https://doi.org/10.1016/0025-5564(94)00067-A
Greenhalgh, D. (1997) Hopf Bifurcation in Epidemic Models with a Latent Period and Nonpermanent Immunity. Mathematical & Computer Modelling, 25, 85-107. https://doi.org/10.1016/S0895-7177(97)00009-5
San-Ling, Y., Han, L.T. and Zhi-En, M.A. (2001) A Kind of Epidemic Model Having Infectious Force in Both Latent Period and Infected Period. Journal of Biomathematics, 16, 392-398.
Zhang, T. and Teng, Z. (2007) On a Nonautonomous Seirs Model in Epidemiology. Bulletin of Mathematical Biology, 69, 2537-2559. https://doi.org/10.1007/s11538-007-9231-z
Daley, D.J. and Kendall, D.G. (1964) Epidemics and Rumours. Nature, 204, 1118. https://doi.org/10.1038/2041118a0
Daley, D.J. and Kendall, D.G. (1965) Stochastic Rumours. IMA Journal of Applied Mathematics, 1, 42-55. https://doi.org/10.1093/imamat/1.1.42
Murray, J.D. (1980) Mathematical Modelling in Epidemiology.
Maki, D.P. and Thompson, M. (1973) Mathematical Models and Applications.
Zanette, D.H. (2001) Critical Behavior of Propagation on Small-World Networks. Physical Review E Statistical Nonlinear & Soft Matter Physics, 64, 1725-1732. https://doi.org/10.1103/PhysRevE.64.050901
Zanette, D.H. (2002) Dynamics of Rumor Propagation on Small-World Networks. Physical Review E, 65, 110-126. https://doi.org/10.1103/PhysRevE.65.041908
Bartolozzi, M., Leinweber, D.B. and Thomas, A.W. (2005) Stochastic Opinion Formation in Scale-Free Networks. Physical Review E Statistical Nonlinear & Soft Matter Physics, 72, 138-148. https://doi.org/10.1103/PhysRevE.72.046113
Simas, T. and Rocha, L.M. (2009) Stochastic Model for Scale-Free Networks with Cutoffs. Physical Review E Statistical Nonlinear & Soft Matter Physics, 78, 837-849.
Isham, V., Harden, S. and Nekovee, M. (2010) Stochastic Epidemics and Rumours on Finite Random Networks. Physica A Statistical Mechanics & Its Applications, 389, 561-576. https://doi.org/10.1103/PhysRevE.72.046113
Hou, Y., Xie, H. and Ma, J. (2013) Stochastic Model of Rumor Spreading in Scale-Free Networks. International Journal of Advancements in Computing Technology, 5, 376-384. https://doi.org/10.4156/ijact.vol5.issue9.45
Kawachi, K. (2008) Deterministic Models for Rumor Transmission. Nonlinear Analysis Real World Applications, 9, 1989-2028. https://doi.org/10.4156/ijact.vol5.issue9.45
Xia, L.L., Jiang, G.P., Song, B., et al. (2015) Rumor Spreading Model Considering Hesitating Mechanism in Complex Social Networks. Physica A Statistical Mechanics & Its Applications, 437, 295-303. https://doi.org/10.1016/j.physa.2015.05.113
Zan, Y., Wu, J., Li, P., et al. (2014) Sicr Rumor Spreading Model in Complex Networks: Counterattack and Self-Resistance. Physica A Statistical Mechanics & Its Applications, 405, 159-170. https://doi.org/10.1016/j.physa.2014.03.021
Gu, J., Li, W. and Cai, X. (2008) The Effect of the Forget-Remember Mechanism on Spreading. European Physical Journal B, 62, 247-255. https://doi.org/10.1140/epjb/e2008-00139-4
Zhao, L., Wang, Q., Cheng, J., et al. (2011) Rumor Spreading Model with Consideration of Forgetting Mechanism: A Case of Online Blogging Live Journal. Physica A Statistical Mechanics & Its Applications, 390, 2619-2625. https://doi.org/10.1016/j.physa.2011.03.010
Zhao, L., Qiu, X., Wang, X., et al. (2013) Rumor Spreading Model Considering Forgetting and Remembering Mechanisms in Inhomogeneous Networks. Physica A Statistical Mechanics & Its Applications, 392, 987-994. https://doi.org/10.1016/j.physa.2012.10.031
Wang, J., Zhao, L. and Huang, R. (2014) 2SI2R Rumor Spreading Model in Homogeneous Networks. Physica A Statistical Mechanics & Its Applications, 413, 153-161. https://doi.org/10.1016/j.physa.2014.06.053