Uncertainty quantification in Covid-19 spread: Lockdown effects

We develop a Bayesian inference framework to quantify uncertainties in epidemiological models. We use SEIJR and SIJR models involving populations of susceptible, exposed, infective, diagnosed, dead and recovered individuals to infer from Covid-19 data rate constants, as well as their variations in response to lockdown measures. To account for confinement, we distinguish two susceptible populations at different risk: confined and unconfined. We show that transmission and recovery rates within them vary in response to facts, and that the diagnose rate is quite low, which leads to large amounts of undiagnosed infective individuals. A key unknown to predict the evolution of the epidemic is the fraction of the population affected by the virus, including asymptomatic subjects. Our study tracks its time evolution with quantified uncertainty from available official data, limited, however, by the data quality. We exemplify the technique with data from Spain, country in which late drastic lockdowns were enforced for months during the first wave of the current pandemic. In late actions and in the absence of other measures, spread is delayed but not stopped unless a large enough fraction of the population is confined until the asymptomatic population is depleted. To some extent, confinement can be replaced by strong distancing through masks in adequate circumstances.