Parameter identification in epidemiological models

We develop a Bayesian inference framework to estimate parameters in epidemiological models with quantified uncertainty. We consider SEIJR models involving populations of susceptible, exposed, infective, diagnosed, dead, and recovered individuals, and infer from data all the parameter models, in particular, the transmission and recovery rates. We exemplify the procedure using Covid-19 data from Spain since the onset of the current pandemic. Successive nonpharmaceutical actions such as lockdowns, distancing, and release of mobility restrictions, define stages in the data which are reflected in the parameter values. Tracking the evolution of the different populations with time, we can infer the evolution of the total fraction of subjects affected by the virus, including asymptomatic individuals. Using the resulting models as constraints in optimization problems for adequate costs we can gain insight on the parameter regimes in which the epidemic would remain controlled, even when migration effects are included.