Metapopulation epidemic models with a universal mobility pattern on interconnected networks

The global pandemic of the coronavirus disease 2019 (COVID-19) exemplifies the influence of human mobility on epidemic spreading. A framework called the movement-interaction-return (MIR) model is a model to study the impact of human mobility on epidemic spreading. In this paper, we investigate epidemic spreading in interconnected metapopulation networks. Specifically, we incorporate the human mobility pattern called the radiation model into the MIR model. As a result, the proposed model is more realistic in comparison to the original MIR model. We use the tensorial framework to develop Markovian equations that describe the dynamics of the proposed model on interconnected metapopulation networks. Then we derive the corresponding epidemic thresholds by converting tensors into matrices. Comprehensive numerical simulations confirm our analysis.