Abstract
The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We develop an individual-based approximation for the susceptible-infected-recovered epidemic model applicable to arbitrary dynamic networks. Our framework provides, at the individual-level, the probability flow over time associated with the infection dynamics. This computationally efficient framework discards the correlation between the states of different nodes, yet provides accurate results in approximating direct numerical simulations. It naturally captures the temporal heterogeneities and correlations of contact sequences, fundamental ingredients regulating the timing and size of an epidemic outbreak, and the number of secondary infections. The high accuracy of our approximation further allows us to detect the index individual of an epidemic outbreak in real-life network data.
Highlights
In the present study, we develop the individual-based approximation (IBA) for the susceptible-infected-recovered model on dynamic contact networks as observed on real settings
We study high-resolution contact network data with Tw = 20 sec, which is much smaller than the time scale of real epidemic processes, in which the infectious period typically lasts a few days or more[28]
The occurrence of epidemic outbreaks typically depends on the pathogen and contact patterns between hosts and susceptible individuals
Summary
We develop the IBA for the susceptible-infected-recovered model on dynamic contact networks as observed on real settings. Our model describes a broad class of infectious diseases, such as measles, chickenpox, and Ebola, where hosts develop immunity or die after a given infectious period[2]. We use our framework to estimate the dynamics of macroscopic epidemiological variables such as the time-dependent prevalence of infections, formulate the effective reproduction number (i.e., the number of secondary infections produced by a single infected individual in a finite population25), quantify super-spreaders[26], and detect the source of infections if past contacts and the epidemiological state of the population are known at a given time[27]
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