Effect of isolation strategies on epidemic spreading in multiplex networks with an annealed interactions layer

When an unprecedented infectious disease with high mortality and transmissibility emerges, immediate access to vaccines or medicines is often unavailable. Therefore, many health authorities rely on non-pharmaceutical interventions, such as contact tracing combined with isolation, to mitigate the spread of the disease. However, contact tracing is generally effective only for well-known fixed contacts such as regular contacts of an individual. In contrast, random and anonymous infections, which are difficult to trace, may still occur, potentially leading to large-scale outbreaks especially when the disease is highly transmissible. In this study, we test the efficacy of isolation based on contact tracing among fixed regular contacts even when untraceable random contacts exist as well. We simulate this scenario using the susceptible-infected-recover model on double-layered multiplex networks, where one layer has a fixed structure, while the other layer is time-varying. Our numerical results indicate that tracing the secondary contacts significantly reduces both the final epidemic size and the number of isolations per unit time, even with imperfect traceability. Our findings suggest that the isolation protocol combined with secondary contact tracing can be an effective measure against unprecedented infectious diseases, applicable to a broad range of fixed contact structures.