Logistic growth on networks: exact solutions for the SI model

  title={Logistic growth on networks: exact solutions for the SI model},
  author={Wout Merbis and Ivano Lodato},
  journal={Physical review. E},
  volume={105 4-1},
The susceptible-infected (SI) model is the most basic of all compartmental models used to describe the spreading of information through a population. Despite its apparent simplicity, the analytic solution of this model on networks is still lacking. We address this problem here using a novel formulation inspired by the mathematical treatment of many-body quantum systems. This allows us to organize the time-dependent expectation values for the state of individual nodes in terms of contributions… 

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