Rumor Propagation Model: An Equilibrium Study

Compartmental epidemiological models have been developed since the 1920s and successfully applied to study the propagation of infectious diseases. Besides, due to their structure, in the 1960s an interesting version of these models was developed to clarify some aspects of rumor propagation, considering that spreading an infectious disease or disseminating information is analogous phenomena. Here, in an analogy with the SIR (Susceptible-Infected-Removed) epidemiological model, the ISS (Ignorant-Spreader-Stifler) rumor spreading model is studied. By using concepts from the Dynamical Systems Theory, stability of equilibrium points is established, according to propagation parameters and initial conditions. Some numerical experiments are conducted in order to validate the model.

[1]  WILLIAM GOFFMAN,et al.  Generalization of Epidemic Theory: An Application to the Transmission of Ideas , 1964, Nature.

[2]  William M. Spears,et al.  A unified prediction of computer virus spread in connected networks , 2002 .

[3]  Yamir Moreno,et al.  Dynamics of rumor spreading in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  D. Kendall,et al.  Epidemics and Rumours , 1964, Nature.

[5]  D. Watts,et al.  Viral marketing for the real world , 2007 .

[6]  W. O. Kermack,et al.  Contributions to the Mathematical Theory of Epidemics. III. Further Studies of the Problem of Endemicity , 1933 .

[7]  C. Watkins,et al.  The spread of awareness and its impact on epidemic outbreaks , 2009, Proceedings of the National Academy of Sciences.

[8]  Stephen A. Greyser,et al.  Sports sponsorship to rally the home team , 2007 .

[9]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[10]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[11]  Bimal Kumar Mishra,et al.  Mathematical models on computer viruses , 2007, Appl. Math. Comput..

[12]  W. O. Kermack,et al.  Contributions to the Mathematical Theory of Epidemics. II. The Problem of Endemicity , 1932 .

[13]  Luiz Henrique Alves Monteiro,et al.  MODELING THE SPREADING OF HIV IN HOMOSEXUAL POPULATIONS WITH HETEROGENEOUS PREVENTIVE ATTITUDE , 2004 .

[14]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[15]  Laurent Massoulié,et al.  Thresholds for virus spread on networks , 2006, valuetools '06.

[16]  Cleve B. Moler,et al.  Numerical computing with MATLAB , 2004 .

[17]  Dan Palmon,et al.  The value of columnists’ stock recommendations: an event study approach , 2009 .

[18]  L M Wahl,et al.  Drug resistance in an immunological model of HIV-1 infection with impulsive drug effects , 2005, Bulletin of mathematical biology.

[19]  José Roberto Castilho Piqueira,et al.  A modified epidemiological model for computer viruses , 2009, Appl. Math. Comput..

[20]  W. O. Kermack,et al.  Contributions to the mathematical theory of epidemics—III. Further studies of the problem of endemicity , 1991 .

[21]  Serge Galam,et al.  Modelling rumors: the no plane Pentagon French hoax case , 2002, cond-mat/0211571.

[22]  Neil F Johnson,et al.  Impact of unexpected events, shocking news, and rumors on foreign exchange market dynamics. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.