  It is a fundamental question in disease modelling how the initial seeding of
an epidemic, spreading over a network, determines its final outcome. Research
in this topic has primarily concentrated on finding the seed configuration
which infects the most individuals. Although these optimal configurations give
insight into how the initial state affects the outcome of an epidemic, they are
unlikely to occur in real life. In this paper we identify two important seeding
scenarios, both motivated by historical data, that reveal a new complex
phenomenon. In one scenario, the seeds are concentrated on the central nodes of
a network, while in the second, they are spread uniformly in the population.
Comparing the final size of the epidemic started from these two initial
conditions through data-driven and synthetic simulations on real and modelled
geometric metapopulation networks, we find evidence for a switchover
phenomenon: When the basic reproduction number $R_0$ is close to its critical
value, more individuals become infected in the first seeding scenario, but for
larger values of $R_0$, the second scenario is more dangerous. We find that the
switchover phenomenon is amplified by the geometric nature of the underlying
network, and confirm our results via mathematically rigorous proofs, by mapping
the network epidemic processes to bond percolation. Our results expand on the
previous finding that in case of a single seed, the first scenario is always
more dangerous, and further our understanding why the sizes of consecutive
waves can differ even if their epidemic characters are similar.
