Stochastic epidemic spreading: not all super-spreading processes are born equal, neither all lockdown strategies

Abstract

We consider viral spreading processes, such as pandemics, in finite networks. For such processes, we propose and analyze a new model which combines two stochastic functions in the spreading intensity of a node, and accounts for two types of super-spreading. The first reflects personal properties of each node and the second reflects occasional spreads in the network. Consequently, studying the spreading dynamics requires the analysis of a stochastic process consisting of those two functions which drastically differ in their dynamics. One (personal) is biasly-modified throughout the process as infected nodes” leave the game” and the distribution of the susceptible population changes. The second (occasional) remains constant throughout the process. We show that the mix between these functions affects dramatically the threshold for the end of the spread (known as the Herd Immunity Threshold, or HIT). We address operational aspects and examine the effectiveness of control mechanisms that restrict the interaction among the population in order to suppress the spread (e.g. lockdowns). We reveal and establish that although different policies might have similar immediate impacts, not all lockdowns are “born equal”, and may drastically differ on the long-term impact: While some reduce the HIT, others may be counter-productive in the long-run and, perhaps surprisingly, increase the HIT.