  In individual SARS-CoV-2 outbreaks, the count of confirmed cases and deaths
follow a Gompertz growth function for locations of very different sizes. This
lack of dependence on region size leads us to hypothesize that virus spread
depends on universal properties of the network of social interactions. We test
this hypothesis by simulating the propagation of a virus on networks of
different topologies. Our main finding is that Gompertz growth observed for
early outbreaks occurs only for a scale-free network, in which nodes with many
more neighbors than average are common. These nodes that have very many
neighbors are infected early in the outbreak and then spread the infection very
rapidly. When these nodes are no longer infectious, the remaining nodes that
have most neighbors take over and continue to spread the infection. In this
way, the rate of spread is fastest at the very start and slows down
immediately. Geometrically it is seen that the "surface" of the epidemic, the
number of susceptible nodes in contact with the infected nodes, starts to
rapidly decrease very early in the epidemic and as soon as the larger nodes
have been infected. In our simulation, the speed and impact of an outbreak
depend on three parameters: the average number of contacts each node makes, the
probability of being infected by a neighbor, and the probability of recovery.
Intelligent interventions to reduce the impact of future outbreaks need to
focus on these critical parameters in order to minimize economic and social
collateral damage.
