Longer-term seeding effects on epidemic processes: a network approach

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.