This study is concerned with the dynamical behaviors of epidemic spreading over a two-layered interconnected network. Three models in different levels are proposed to describe cooperative spreading processes over the interconnected network, wherein the disease in one network can spread to the other. Theoretical analysis is provided for each model to reveal that the global epidemic threshold in the interconnected network is not larger than the epidemic thresholds for the two isolated layered networks. In particular, in an interconnected homogenous network, detailed theoretical analysis is presented, which allows quick and accurate calculations of the global epidemic threshold. Moreover, in an interconnected heterogeneous network with inter-layer correlation between node degrees, it is found that the inter-layer correlation coefficient has little impact on the epidemic threshold, but has significant impact on the total prevalence. Simulations further verify the analytical results, showing that cooperative epidemic processes promote the spreading of diseases.
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