In this paper we touch upon three phenomena observed in real life as well as in simulations;
in one case, we state mathematical
results about the appearance of the phenomenon on arbitrary graphs (networks) under
rather general conditions. We discuss
a phenomenon of critical fluctuations, demonstrating that an epidemic can behave very
differently even if it runs on the same
network, with the same transmission probabilities and started from the same initial
seeds. We explore a connection between
the geographic distribution and intensity of the spreading epidemic. We argue that
the speed of the spread of an epidemic
depends not only on the number of current infections, but also on their geographic
distribution over a country. Through the
observations of these phenomena we suggest a dependence of the final epidemic size
on the geometric position of initial seeds
of an epidemic process.
