Eur. Phys. J. B (2015) 88: 341
https://doi.org/10.1140/epjb/e2015-60620-5

Regular Article

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

¹ Sorbonne Universités, UPMC Univ. Paris 06, INSERM, Institut Pierre Louis d’Épidémiologie et de Santé Publique (IPLESP, UMRS 1136), 75012 Paris, France
² ISI Foundation, 10126 Torino, Italy

^b e-mail: vittoria.colizza@inserm.fr

Received: 31 July 2015
Received in final form: 27 October 2015
Published online: 21 December 2015

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 [E. Valdano, L. Ferreri, C. Poletto, V. Colizza, Phys. Rev. X 5, 21005 (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.