Synchronization in epidemic growth and the impossibility of selective containment

• Main Authors: Bergholtz, E.J (Author), Budich, J.C (Author)
• Format: Article
• Language: English
• Published: Oxford University Press 2021
• Subjects: Epidemic dynamics; Epidemiology; Growth behavior; Non-pharmaceutical interventions; Risk groups; Scaling factors; Simple modeling
• Online Access: View Fulltext in Publisher

 Containment, aiming to prevent the epidemic stage of community-spreading altogether, and mitigation, aiming to merely 'flatten the curve' of a wide-ranged outbreak, constitute two qualitatively different approaches to combating an epidemic through non-pharmaceutical interventions. Here, we study a simple model of epidemic dynamics separating the population into two groups, namely a low-risk group and a high-risk group, for which different strategies are pursued. Due to synchronization effects, we find that maintaining a slower epidemic growth behaviour for the high-risk group is unstable against any finite coupling between the two groups. More precisely, the density of infected individuals in the two groups qualitatively evolves very similarly, apart from a small time delay and an overall scaling factor quantifying the coupling between the groups. Hence, selective containment of the epidemic in a targeted (high-risk) group is practically impossible whenever the surrounding society implements a mitigated community-spreading. We relate our general findings to the ongoing COVID-19 pandemic. © 2021 The Author(s) 2021. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications.