Estimating required ‘lockdown’ cycles before immunity to SARS-CoV-2: model-based analyses of susceptible population sizes, ‘S0’, in seven European countries, including the UK and Ireland

Abstract

Background: Following stringent social distancing measures, some European countries are beginning to report a slowed or negative rate of growth of daily case numbers testing positive for the novel coronavirus. The notion that the first wave of infection is close to its peak begs the question of whether future peaks or ‘second waves’ are likely. We sought to determine the current size of the effective (i.e. susceptible) population for seven European countries—to estimate immunity levels following this first wave. Methods: We used Bayesian model inversion to estimate epidemic parameters from the reported case and death rates from seven countries using data from late January 2020 to April 5th 2020. Two distinct generative model types were employed: first a continuous time dynamical-systems implementation of a Susceptible-Exposed-Infectious-Recovered (SEIR) model, and second a partially observable Markov Decision Process or hidden Markov model (HMM) implementation of an SEIR model. Both models parameterise the size of the initial susceptible population (‘S0’), as well as epidemic parameters. Results: Both models recapitulated the dynamics of transmissions and disease as given by case and death rates. Crucially, maximum a posteriori estimates of S0 for each country indicated effective population sizes of below 20% (of total population size), under both the continuous time and HMM models. Using a Bayesian weighted average across all seven countries and both models, we estimated that 6.4% of the total population would be immune. From the two models, the maximum percentage of the effective population was estimated at 19.6% of the total population for the UK, 16.7% for Ireland, 11.4% for Italy, 12.8% for Spain, 18.8% for France, 4.7% for Germany and 12.9% for Switzerland. Conclusion: Our results indicate that after the current wave, a large proportion of the total population will remain without immunity.