Modelling lockdown-induced 2nd COVID waves in France

As with the Spanish Flu a century ago, authorities have responded to the current COVID-19 pandemic with extraordinary public health measures. In particular, lockdown and related social distancing policies are motivated in some countries by the need to slow virus propagation--so that the primary wave of patients suffering from severe forms of COVID infection do not exceed the capacity of intensive care units. But unlocking poses a critical issue because relaxing social distancing may, in principle, generate secondary waves. Ironically however, the dynamic repertoire of established epidemiological models that support this kind of reasoning is limited to single epidemic outbreaks. In turn, predictions regarding secondary waves are tautologically derived from imposing assumptions about changes in the so-called "effective reproduction number". In this work, we depart from this approach and extend the LIST (Location-Infection-Symptom-Testing) model of the COVID pandemic with realistic nonlinear feedback mechanisms that under certain conditions, cause lockdown-induced secondary outbreaks. The original LIST model captures adaptive social distancing, i.e. the transient reduction of the number of person-to-person contacts (and hence the rate of virus transmission), as a societal response to salient public health risks. Here, we consider the possibility that such pruning of socio-geographical networks may also temporarily isolate subsets of local populations from the virus. Crucially however, such unreachable people will become susceptible again when adaptive social distancing relaxes and the density of contacts within socio-geographical networks increases again. Taken together, adaptive social distancing and network unreachability thus close a nonlinear feedback loop that endows the LIST model with a mechanism that can generate autonomous (lockdown-induced) secondary waves. However, whether and how secondary waves arise depend upon the interaction with other nonlinear mechanisms that capture other forms of transmission heterogeneity. We apply the ensuing LIST model to numerical simulations and exhaustive analyses of regional French epidemiological data. In brief, we find evidence for this kind of nonlinear feedback mechanism in the empirical dynamics of the pandemic in France. However, rather than generating catastrophic secondary outbreaks (as is typically assumed), the model predicts that the impact of lockdown-induced variations in population susceptibility and transmission may eventually reduce to a steady-state endemic equilibrium with a low but stable infection rate.