Competitive epidemic networks with multiple survivalofthefittest outcomes
Abstract
We use a deterministic model to study two competing viruses spreading over a twolayer network in the SusceptibleInfectedSusceptible (SIS) framework, and address a central problem of identifying the winning virus in a "survivalofthefittest" battle. Existing sufficient conditions ensure that the same virus always wins regardless of initial states. For networks with an arbitrary but finite number of nodes, there exists a necessary and sufficient condition that guarantees local exponential stability of the two equilibria corresponding to each virus winning the battle, meaning that either of the viruses can win, depending on the initial states. However, establishing existence and finding examples of networks with more than three nodes that satisfy such a condition has remained unaddressed. In this paper, we prove that, for any arbitrary number of nodes, such networks exist. We do this by proving that given almost any network layer of one virus, there exists a network layer for the other virus such that the resulting twolayer network satisfies the aforementioned condition. To operationalize our findings, a fourstep procedure is developed to reliably and consistently design one of the network layers, when given the other layer. Conclusions from numerical case studies, including a realworld mobility network that captures the commuting patterns for people between $107$ provinces in Italy, extend on the theoretical result and its consequences.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 arXiv:
 arXiv:2111.06538
 Bibcode:
 2021arXiv211106538Y
 Keywords:

 Mathematics  Dynamical Systems;
 Electrical Engineering and Systems Science  Systems and Control
 EPrint:
 Submitted to Physical Review E on 2021Nov02. Revised version submitted 2022Sept22