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# Approaches to epidemiological models on complex temporal networks

Abstract:

The objective of our work is to examine paths for the spread of infectious diseases on a given temporal network. The latter is a simple model, which abstracts the contact dynamics within a population. An edge thus appears as long as two individuals are in physical proximity. Recently, a matrix formalism has been introduced in order to compute the path structure of infectious diseases that can traverse a temporal network even after arbitrary waiting times, i.e. a SI-model (susceptible-infected-model). Many infectious diseases, however, possess a finite infectious period, i.e. the time period after which the infection dies out, if it is not passed on. This can be regarded as a SIS or SIR (susceptible-infected-recovered) model, respectively. In this work, we introduce a novel matrix formalism that allows for explicit consideration of finite infectious periods. In order to demonstrate the capabilities of the approach we apply the formalism to two real-world temporal networks and calculate central properties from statistical epidemiology.