  Recently, some studies have revealed that non-Poissonian statistics of human
behaviors stem from the hierarchical geographical network structure. On this
view, we focus on epidemic spreading in the hierarchical geographical networks,
and study how two distinct contact patterns (i. e., homogeneous time delay
(HOTD) and heterogeneous time delay (HETD) associated with geographical
distance) influence the spreading speed and the variability of outbreaks. We
find that, compared with HOTD and null model, correlations between time delay
and network hierarchy in HETD remarkably slow down epidemic spreading, and
result in a upward cascading multi-modal phenomenon. Proportionately, the
variability of outbreaks in HETD has the lower value, but several comparable
peaks for a long time, which makes the long-term prediction of epidemic
spreading hard. When a seed (i. e., the initial infected node) is from the high
layers of networks, epidemic spreading is remarkably promoted. Interestingly,
distinct trends of variabilities in two contact patterns emerge: high-layer
seeds in HOTD result in the lower variabilities, the case of HETD is opposite.
More importantly, the variabilities of high-layer seeds in HETD are much
greater than that in HOTD, which implies the unpredictability of epidemic
spreading in hierarchical geographical networks.
