Synchronization in epidemic growth and the impossibility of selective containment

Math Med Biol. 2021 Dec 15;38(4):467-473. doi: 10.1093/imammb/dqab013.


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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • COVID-19*
  • Humans
  • Pandemics*
  • Risk Factors
  • SARS-CoV-2