Article http://dx.doi.org/10.26855/jamc.2021.06.005

IVESR Rumor Spreading Model in Homogeneous Network with Hesitating and Forgetting Mechanisms


Md. Nahid Hasan, Saiful Islam*, Chandra Nath Podder

Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh.

*Corresponding author: Saiful Islam

Published: May 21,2021


In this paper, we study a new IVESR rumor spreading model with hesitating and forgetting mechanisms in homogeneous network. The rumor free and rumor prevailing equilibriums, and the basic reproduction number  are calculated from the mean-field equations of the model. The local and global stability of rumor free equilibrium are proved by using Lyapunov function and LaSalle invariance principle, and the existence of rumor prevailing equilibrium is shown. In numerical simulations, it is found that the vaccination, prohibiting people to spread the rumor, can lessen the propagation of rumor in the network. We also show that the fuzziness of the rumor has a great impact on the size of spreader and the forgetting factor has a great effect on the rumor prevailing duration. Furthermore, we analyze the sensitivity of different parameters on  and discussed how they affect the spreading and controlling of the rumor.


[1] Galam, S. (2003). Modelling rumors: the no plane Pentagon French hoax case. Physica A: Statistical Mechanics and Its Applications, 2003, 320: 571-580.

[2] Hayakawa, H. (2002). Sociology of rumor-approach from formal sociology. Seikyusya, Tokyo, 2002.

[3] Kimmel, A. J. (2004). Rumors and rumor control: A manager’s guide to understanding and combatting rumors. Routledge.

[4] Kosfeld, M. (2005). Rumours and markets. Journal of Mathematical Economics, 2005, 41(6): 646-664.

[5] Kawachi, K. (2008). Deterministic models for rumor transmission. Nonlinear analysis: Real world applications, 2008, 9(5): 1989-2028.

[6] Misra, A. K. (2012). A simple mathematical model for the spread of two political parties. Nonlinear Analysis: Modelling and Control, 2012, 17(3): 343-354.

[7] Daley, D. J. and D. G. Kendall. (1964). Epidemics and rumours. Nature, 1964, 204(4963): 1118-1118.

[8] Kimmel, A. J. (2004). Rumors and the financial marketplace. The Journal of Behavioral Finance, 2004, 5(3): 134-141.

[9] Barabási, A.-L. and R. Albert. (1999). Emergence of scaling in random networks. Science, 1999, 286(5439): 509-512.

[10] Kesten, H. and V. Sidoravicius. (2005). The spread of a rumor or infection in a moving population. Annals of Probability, 2005, 33(6): 2402-2462.

[11] Daley, D. J. and D. G. Kendall. (1965). Stochastic rumours. IMA Journal of Applied Mathematics, 1965, 1(1): 42-55.

[12] Maki, D. P. and M. Thompson. (1973). Mathematical models and applications: with emphasis on the social life, and management sciences. 

[13] Nekovee, M., et al. (2007). Theory of rumour spreading in complex social networks. Physica A: Statistical Mechan-ics and its Applications, 2007, 374(1): 457-470.

[14] Isham, V., S. Harden, and M. Nekovee. (2010). Stochastic epidemics and rumours on finite random networks. Physica A: Statistical Mechanics and its Applications, 2010, 389(3): 561-576.

[15] Gu, J. and X. Cai. (2007). The forget-remember mechanism for 2-state spreading. arXiv preprint nlin/0702021.

[16] Gu, J., W. Li, and X. Cai. (208). The effect of the forget-remember mechanism on spreading. The European Physical Journal B, 2008, 62(2): 247-255.

[17] Zhao, L., et al. (2013). Rumor spreading model considering forgetting and remembering mechanisms in inhomoge-neous networks. Physica A: Statistical Mechanics and its Applications, 2013, 392(4): 987-994.

[18] Zhao, L., et al. (2012). SIHR rumor spreading model in social networks. Physica A: Statistical Mechanics and its Applications, 2012, 391(7): 2444-2453.

[19] Wan, C., T. Li, and Z. Sun. (2017). Global stability of a SEIR rumor spreading model with demographics on scale-free networks. Advances in Difference Equations, 2017(1): 1-15.

[20] Liu, X., T. Li, and M. Tian. (2018). Rumor spreading of a SEIR model in complex social networks with hesitating mechanism. Advances in Difference Equations, 2018(1): 1-24.

[21] Zhou, Y., et al. (2019). Rumor source detection in networks based on the SEIR model. IEEE access, 2019, 7: 45240-45258.

[22] Lakshmikantham, V., S. Leela, and A. A. Martynyuk. (1989). Stability analysis of nonlinear systems. 1989: Sprin-ger.

[23] Hethcote, H. W. (2000). The mathematics of infectious diseases. SIAM review, 2000, 42(4): 599-653.

[24] Van den Driessche, P. and J. Watmough. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical biosciences, 2002, 180(1-2): 29-48.

[25] Hale, J. (1969). Ordinary Differential Equations Wiley. New York. 1969.

[26] La Salle, J. P. (1976). The stability of dynamical systems. 1976: SIAM.

[27] Chitnis, N., J. M. Hyman, and J. M. Cushing. (2008). Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bulletin of Mathematical Biology, 2008, 70(5): 1272.

How to cite this paper

IVESR Rumor Spreading Model in Homogeneous Network with Hesitating and Forgetting Mechanisms

How to cite this paper: Md. Nahid Hasan, Saiful Islam, Chandra Nath Podder. (2021) IVESR Rumor Spreading Model in Homogeneous Network with Hesitating and Forgetting Mechanisms. Journal of Applied Mathematics and Computation5(2), 105-118.

DOI: http://dx.doi.org/10.26855/jamc.2021.06.005