Infection propagator approach to compute epidemic thresholds on temporal networks: impact of immunity and of limited temporal resolution

TL;DR

This paper introduces an infection propagator method to accurately compute epidemic thresholds on temporal networks, considering immunity and limited temporal resolution, and demonstrates its effectiveness through models and real-world data.

Contribution

It extends the infection propagator framework to include effects of immunity and temporal resolution limitations, improving epidemic threshold predictions.

Findings

Immunity does not affect epidemic threshold estimates.

Aggregation of temporal data reduces prediction accuracy for fast diseases.

Preserving weight-topology correlations enhances prediction accuracy.

Abstract

The epidemic threshold of a spreading process indicates the condition for the occurrence of the wide spreading regime, thus representing a predictor of the network vulnerability to the epidemic. Such threshold depends on the natural history of the disease and on the pattern of contacts of the network with its time variation. Based on the theoretical framework introduced in (Valdano et al. PRX 2015) for a susceptible-infectious-susceptible model, we formulate here an infection propagator approach to compute the epidemic threshold accounting for more realistic effects regarding a varying force of infection per contact, the presence of immunity, and a limited time resolution of the temporal network. We apply the approach to two temporal network models and an empirical dataset of school contacts. We find that permanent or temporary immunity do not affect the estimation of the epidemic threshold through the infection propagator approach. Comparisons with numerical results show the good agreement of the analytical predictions. Aggregating the temporal network rapidly deteriorates the predictions, except for slow diseases once the heterogeneity of the links is preserved. Weight-topology correlations are found to be the critical factor to be preserved to improve accuracy in the prediction.