Mixed distribution model of human communication and its impacts on the spreading process

¹ School of Science, Beijing University of Posts and Telecommunications - Beijing, China
² Departament de Física de la Matèria Condensada, Universitat de Barcelona - Martí i Franquès 1, 08028 Barcelona, Spain
³ Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona - Barcelona, Spain

^(a) zhengmuhua163@gmail.com
^(b) jhxiao@bupt.edu.cn

Received: 6 November 2019
Accepted: 5 February 2020

Abstract

The heterogeneous inter-event time of human contacts may fundamentally alter spreading dynamics. This generally assumes that the inter-event time distribution can be depicted with power-law–like decays. In empirical human communication data, the shape of the inter-event distribution is more complicated. Particularly, both the head and the tail of the inter-event distribution deviates from the power-law–like decay. In this paper, we examine two communication databases and propose a mixed distribution to depict the inter-event distributions, which agrees better with the empirical data. We then show how the inter-event distributions shape the co-evolved SIR spreading. Especially, the SIR dynamical equations are extended to adapt to the general inter-event distribution via introducing the new infected rate. By a numerical analysis of the newly infected individuals at each time step, we illustrate how the spreading size is determined by the inter-event time distribution and the parameters of the SIR dynamic.