A network epidemic model for online community commissioning data

A statistical model assuming a preferential attachment network, which is generated by adding nodes sequentially according to a few simple rules, usually describes real-life networks better than a model assuming, for example, a Bernoulli random graph, in which any two nodes have the same probability of being connected, does. Therefore, to study the propagation of “infection” across a social network, we propose a network epidemic model by combining a stochastic epidemic model and a preferential attachment model. A simulation study based on the subsequent Markov Chain Monte Carlo algorithm reveals an identifiability issue with the model parameters. Finally, the network epidemic model is applied to a set of online commissioning data.

[1]  F. Ball,et al.  Epidemics with two levels of mixing , 1997 .

[2]  Piet Van Mieghem,et al.  Epidemic processes in complex networks , 2014, ArXiv.

[3]  Adam Tauman Kalai,et al.  Graph model selection using maximum likelihood , 2006, ICML.

[4]  D. Hunter,et al.  Bayesian Inference for Contact Networks Given Epidemic Data , 2010 .

[5]  Naoki Masuda,et al.  A Gillespie Algorithm for Non-Markovian Stochastic Processes , 2016, SIAM Rev..

[6]  P. O’Neill,et al.  Inference for Epidemics with Three Levels of Mixing: Methodology and Application to a Measles Outbreak , 2011 .

[7]  Tom A. B. Snijders,et al.  Markov Chain Monte Carlo Estimation of Exponential Random Graph Models , 2002, J. Soc. Struct..

[8]  Gavin J. Gibson,et al.  Statistical inference for stochastic epidemic models , 2002 .

[9]  Fei Xiang,et al.  Efficient MCMC for temporal epidemics via parameter reduction , 2014, Comput. Stat. Data Anal..

[10]  Gareth O. Roberts,et al.  Non-centred parameterisations for hierarchical models and data augmentation. , 2003 .

[11]  Patrick Olivier,et al.  App Movement: A Platform for Community Commissioning of Mobile Applications , 2016, CHI.

[12]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[13]  Philip D O'Neill,et al.  A tutorial introduction to Bayesian inference for stochastic epidemic models using Markov chain Monte Carlo methods. , 2002, Mathematical biosciences.

[14]  PETER NEAL,et al.  A case study in non-centering for data augmentation: Stochastic epidemics , 2005, Stat. Comput..

[15]  D. Hunter,et al.  Goodness of Fit of Social Network Models , 2008 .

[16]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[17]  Carsten Wiuf,et al.  Subnets of scale-free networks are not scale-free: sampling properties of networks. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[18]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[19]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[20]  Joseph Gani,et al.  Stochastic Epidemic Models and Their Statistical Analysis , 2002 .

[21]  Darren J. Wilkinson Stochastic Modelling for Systems Biology , 2006 .

[22]  P. O’Neill,et al.  Bayesian inference for stochastic epidemics in populations with random social structure , 2002 .

[23]  Alessandro Vespignani,et al.  Large-scale topological and dynamical properties of the Internet. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[25]  M. J. Bayarri,et al.  Non-Centered Parameterisations for Hierarchical Models and Data Augmentation , 2003 .

[26]  Youssef M. Marzouk,et al.  A Bayesian method for inferring transmission chains in a partially observed epidemic. , 2008 .

[27]  David Welch,et al.  A Network‐based Analysis of the 1861 Hagelloch Measles Data , 2012, Biometrics.