Abstract
The transmission of pathogen between hosts and the interactions among hosts are two crucial factors for the spreading of epidemics. The former process is generally non-Markovian as the amount of the pathogen developed in hosts undergoes complicated biological process, while the latter one is time-varying due to the dynamic nature of modern society. Despite the abundant efforts working on the effects of the two aspects, a framework that integrates these two factors in a unified representation is still missing. In this paper, we develop a framework with tensorial description encoding non-Markovian process and temporal structure by introducing a super-matrix representation that incorporates multiple discrete time steps in a chronological order. Our proposed framework formulated with super-matrix representation allows a general analytical derivation of the epidemic threshold in terms of the spectral radius of the super-matrix. The accuracy of the approach is verified by different temporal network models. This framework could serve as an effective tool to offer novel understanding of integrated dynamics induced from non-Markovian individual processes and temporal interacting structures.
Published Version
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