The free boundary problem describing information diffusion in online social networks

Abstract In this paper we consider a free boundary problem for a reaction–diffusion logistic equation with a time-dependent growth rate. Such a problem arises in the modeling of information diffusion in online social networks, with the free boundary representing the spreading front of news among users. We present several sharp thresholds for information diffusion that either lasts forever or suspends in finite time. In the former case, we give the asymptotic spreading speed which is determined by a corresponding elliptic equation.

[1]  Haiyan Wang,et al.  On the Existence of Positive Solutions of Fourth-Order Ordinary Differential Equations , 1995 .

[2]  Jure Leskovec,et al.  Modeling Information Diffusion in Implicit Networks , 2010, 2010 IEEE International Conference on Data Mining.

[3]  James D. Murray.  Mathematical Biology: I. An Introduction , 2007 .

[4]  L. I. Rubinshteĭn.  The Stefan Problem , 1971 .

[5]  D. Tarzia,et al.  Asymptotic behavior of the solutions of the dead-core problem , 1989 .

[6]  Yihong Du,et al.  Spreading–vanishing dichotomy in a diffusive logistic model with a free boundary, II☆ , 2011 .

[7]  Anja Feldmann,et al.  Understanding online social network usage from a network perspective , 2009, IMC '09.

[8]  Krishna P. Gummadi,et al.  Characterizing social cascades in flickr , 2008, WOSN '08.

[9]  Balachander Krishnamurthy,et al.  Network level footprints of facebook applications , 2009, IMC '09.

[10]  Ben Y. Zhao,et al.  Understanding latent interactions in online social networks , 2010, IMC '10.

[11]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[12]  Yihong Du,et al.  Logistic Type Equations on RN by a Squeezing Method Involving Boundary Blow‐Up Solutions , 2001 .

[13]  Chen-Nee Chuah,et al.  Unveiling facebook: a measurement study of social network based applications , 2008, IMC '08.

[14]  Kristina Lerman,et al.  A framework for quantitative analysis of cascades on networks , 2010, WSDM '11.

[15]  Alimardon Elmurodov,et al.  Free boundary problem for predator-prey model , 2023, E3S Web of Conferences.

[16]  A. M. Meirmanov,et al.  The Stefan Problem , 1992 .

[17]  C. Cosner,et al.  Spatial Ecology via Reaction-Diffusion Equations , 2003 .

[18]  Kristina Lerman,et al.  Information Contagion: An Empirical Study of the Spread of News on Digg and Twitter Social Networks , 2010, ICWSM.

[19]  Avner Friedman,et al.  A Free Boundary Problem Arising in a Model of Wound Healing , 2000, SIAM J. Math. Anal..

[20]  Kristina Lerman,et al.  What Stops Social Epidemics? , 2011, ICWSM.

[21]  Yihong Du,et al.  Spreading-Vanishing Dichotomy in the Diffusive Logistic Model with a Free Boundary , 2010, SIAM J. Math. Anal..

[22]  Shyhtsun Felix Wu,et al.  Measuring message propagation and social influence on Twitter.com , 2010, Int. J. Commun. Networks Distributed Syst..

[23]  Virgílio A. F. Almeida,et al.  Characterizing user behavior in online social networks , 2009, IMC '09.