Group-Based General Epidemic Modeling for Spreading Processes on Networks: GroupGEM

We develop a group-based continuous-time Markov general epidemic modeling (GroupGEM) framework for any compartmental epidemic model (e.g., susceptible-infected-susceptible, susceptible-infected-recovered, susceptible-exposed-infected-recovered). Here, a group consists of a collection of individual nodes of a network. This model can be used to understand the critical dynamic characteristics of a stochastic epidemic spreading over large complex networks while being informative about the state of groups. Aggregating nodes by groups, the state-space becomes smaller than the one of individual-based approach at the cost of an aggregation error, which is bounded by the well-known isoperimetric inequality. We also develop a mean-field approximation of this framework to reduce the state-space size further. Finally, we extend the GroupGEM to multilayer networks. Individual-based frameworks are in general not computationally efficient. However, the individual-based approach is essential when the objective is to study the local dynamics at the individual level. Therefore, we propose a group-based framework to reduce the computational time of the Individual-based generalized epidemic modeling framework (GEMF) but retain its advantages.