Analysis of the susceptible-infected-susceptible epidemic dynamics in networks via the non-backtracking matrix

@article{Masuda2020AnalysisOT,
  title={Analysis of the susceptible-infected-susceptible epidemic dynamics in networks via the non-backtracking matrix},
  author={Naoki Masuda and Masaki Ogura and Victor M. Preciado},
  journal={ArXiv},
  year={2020},
  volume={abs/1906.04269}
}
We study the stochastic susceptible-infected-susceptible model of epidemic processes on finite directed and weighted networks with arbitrary structure. We present a new lower bound on the exponential rate at which the probabilities of nodes being infected decay over time. This bound is directly related to the leading eigenvalue of a matrix that depends on the non-backtracking and incidence matrices of the network. The dimension of this matrix is $N+M$, where $N$ and $M$ are the number of… 

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