Abstract
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.
Highlights
Social network analysis has been a popular research topic over the last couple of decades, thanks to the unprecedentedly large amount of internet data available, and the increasing power of computers to deal with such data, which details ties between people or objects all over the world
In the statistical literature is the exponential random graph model (ERGM), in which the probability mass function on the graph space is proportional to the exponential of a linear combination of graph statistics; see, for example, Snijders (2002)
In view of the differences in objectives and applications shown above, we propose a network epidemic model as an attempt to narrow the gap in the literature
Summary
Social network analysis has been a popular research topic over the last couple of decades, thanks to the unprecedentedly large amount of internet data available, and the increasing power of computers to deal with such data, which details ties between people or objects all over the world. The infectious period and the contacts made by an infected individual are assumed to follow an exponential distribution and a homogeneous Poisson process, respectively. While these assumptions may be unrealistic for real-life data, they are useful as the epidemic process is Markovian. We focus on a susceptible-infectious (SI) model, in which the epidemic process takes place on a network which is assumed to be built from the PA model, deviating from a BRG When it comes to inference, the data contain the infection times and potentially the transmission tree, while the underlying network is unknown and treated as latent variables. Such an assumption is reasonable because the timescale of an epidemic is usually much smaller than that of network formation, the process of which is described
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