Artículos de revistas
A Connection Between A System Of Random Walks And Rumor Transmission
Registro en:
Physica A: Statistical Mechanics And Its Applications. , v. 392, n. 23, p. 5793 - 5800, 2013.
3784371
10.1016/j.physa.2013.07.073
2-s2.0-84884673634
Autor
Lebensztayn E.
Rodriguez P.M.
Institución
Resumen
We establish a relationship between the phenomenon of rumor transmission on a population and a probabilistic model of interacting particles on the complete graph. More precisely, we consider variations of the Maki-Thompson epidemic model and the "frog model" of random walks, which were introduced in the scientific literature independently and in different contexts. We analyze the Markov chains which describe these models, and show a coupling between them. Our connection shows how the propagation of a rumor in a closed homogeneously mixing population can be described by a system of random walks on the complete graph. Additionally, we discuss further applications of the random walk model which are relevant to the modeling of different biological dynamics. © 2013 Elsevier B.V. All rights reserved. 392 23 5793 5800 Alves, O.S.M., MacHado, F.P., Popov, S., Phase transition for the frog model (2002) Electron. J. Probab., 7 (16), pp. 1-21 Alves, O.S.M., MacHado, F.P., Popov, S., The shape theorem for the frog model (2002) Ann. Appl. Probab., 12 (2), pp. 533-546 Lebensztayn, E., MacHado, F.P., Popov, S., An improved upper bound for the critical probability of the frog model on homogeneous trees (2005) J. Stat. Phys., 119 (12), pp. 331-345 Lebensztayn, E., MacHado, F.P., Martinez, M.Z., Nonhomogeneous random walks systems on Z (2010) J. Appl. Probab., 47, pp. 562-571 Alves, O.S.M., Lebensztayn, E., MacHado, F.P., Martinez, M.Z., Random walks systems on complete graphs (2006) Bull. Braz. Math. Soc., 37 (4), pp. 571-580 Kurtz, T.G., Lebensztayn, E., Leichsenring, A.R., MacHado, F.P., Limit theorems for an epidemic model on the complete graph (2008) ALEA, 4, pp. 45-55 MacHado, F.P., Matzinger, H., Mashurian, H., CLT for the proportion of infected individuals for an epidemic model on a complete graph (2011) Markov Process. Related Fields, 17, pp. 209-224 Maki, D.P., Thompson, M., (1973) Mathematical Models and Applications. with Emphasis on the Social, Life, and Management Sciences, , Prentice-Hall Englewood Cliffs, N. J Daley, D.J., Kendall, D.G., Epidemics and rumours (1964) Nature, 204, p. 1118 Daley, D.J., Gani, J., (1999) Epidemic Modelling: An Introduction, , Cambridge University Press Cambridge Sudbury, A., The proportion of the population never hearing a rumour (1985) J. Appl. Probab., 22, pp. 443-446 Watson, R., On the size of a rumour (1988) Stochastic Process. Appl., 27, pp. 141-149 Belen, S., Pearce, C.E.M., Rumours with random initial conditions (2004) ANZIAM J., 45, pp. 393-400 Coletti, C.F., Rodriguez, P.M., Schinazi, R.B., A spatial stochastic model for rumor transmission (2012) J. Stat. Phys., 147 (2), pp. 375-381 Nekovee, M., Moreno, Y., Bianconi, G., Marsili, M., Theory of rumour spreading in complex social networks (2007) Physica A, 374, pp. 457-470 Moreno, Y., Nekovee, M., Pacheco, A., Dynamics of rumor spreading in complex networks (2004) Phys. Rev. e, 69, p. 066130 Zanette, D.H., Critical behavior of propagation on small-world networks (2001) Phys. Rev. e, 64, pp. 050901R Zanette, D.H., Dynamics of rumour propagation on small-world networks (2002) Phys. Rev. e, 65, p. 041908 Lebensztayn, E., MacHado, F.P., Rodríguez, P.M., On the behaviour of a rumour process with random stifling (2011) Environ. Modell. Softw., 26 (4), pp. 517-522 Belen, S., (2008) The Behaviour of Stochastic Rumours, , Ph.D. Thesis, School of Mathematical Sciences, University of Adelaide, Australia Odagiri, K., Takatsuka, K., Threshold effect with stochastic fluctuation in bacteria-colony-like proliferation dynamics as analyzed through a comparative study of reaction-diffusion equations and cellular automata (2009) Phys. Rev. e, 79, p. 026202