Network localization is unalterable by infections in bursts

Abstract

To shed light on the disease localization phenomenon, we study a bursty susceptible-infected-susceptible (SIS) model and analyze the model under the mean-field approximation. In the bursty SIS model, the infected nodes infect all their neighbors periodically, and the near-threshold steady-state prevalence is non-constant and maximized by a factor equal to the largest eigenvalue ${\lambda }_1$ of the adjacency matrix of the network. We show that the maximum near-threshold prevalence of the bursty SIS process on a localized network tends to zero even if ${\lambda }_1$ diverges in the thermodynamic limit, which indicates that the burst of infection cannot turn a localized spreading into a delocalized spreading. Our result is evaluated both on synthetic and real networks.

11 pages (6 pages for main text and 5 pages for appendix), 9 figures (2 figures in main text and 7 figures in appendix) and 1 table in appendix; Modifications made in the main text: simulations added (Sec. 4.2; In Fig.2(b), the original networks with $\gamma =3$ in Version 1 around 10^2 and 10^3 have lost and this two networks are regenerated), references added. No changes in the appendix