Abstract
Given the adjacency matrix of a network, we present a second-order mean-field expansion that improves on the first-order -intertwined susceptible-infected-susceptible (SIS) epidemic model. Unexpectedly, we found that, in contrast to first-order, second-order mean-field theory is not always possible: the network size should be large enough. Under the assumption of large , we show that the crucial and characterizing quantity, the SIS epidemic threshold , obeys an eigenvalue equation, more complex than the one in the first-order -intertwined model. However, the resulting epidemic threshold is more accurate: , where the first-order epidemic threshold is and where is the spectral radius of the adjacency matrix .
- Received 23 December 2011
DOI:https://doi.org/10.1103/PhysRevE.85.056111
©2012 American Physical Society