Contact tracing-induced Allee effect in disease dynamics

Matías Arim, Daniel Herrera-Esposito, Paola Bermolen, Alvaro Cabana, María Ines Fariello, Mauricio Lima, Hector Romero

Abstract:

Contact tracing, case isolation, quarantine, social distancing, and other non-pharmaceutical interventions
(NPIs) have been a cornerstone in managing the COVID-19 pandemic. However, their effects on disease
dynamics are not fully understood. Saturation of contact tracing caused by the increase of infected indi-
viduals has been recognized as a crucial variable by healthcare systems worldwide. Here, we model this
saturation process with a mechanistic and a phenomenological model and show that it induces an Allee
effect which could determine an infection threshold between two alternative states—containment and
outbreak. This transition was considered elsewhere as a response to the strength of NPIs, but here we
show that they may be also determined by the number of infected individuals. As a consequence, timing
of NPIs implementation and relaxation after containment is critical to their effectiveness. Containment
strategies such as vaccination or mobility restriction may interact with contact tracing-induced Allee
effect. Each strategy in isolation tends to show diminishing returns, with a less than proportional effect
of the intervention on disease containment. However, when combined, their suppressing potential is
enhanced. Relaxation of NPIs after disease containment--e.g. because vaccination--have to be performed
in attention to avoid crossing the infection threshold required to a novel outbreak. The recognition of a
contact tracing-induced Allee effect, its interaction with other NPIs and vaccination, and the existence of
tipping points contributes to the understanding of several features of disease dynamics and its response
to containment interventions. This knowledge may be of relevance for explaining the dynamics of dis-
eases in different regions and, more importantly, as input for guiding the use of NPIs, vaccination cam-
paigns, and its combination for the management of epidemic outbreaks.