Covid-19 Belgium: Extended SEIR-QD model with nursing homes and long-term scenarios-based forecasts

Following the spread of the covid-19 pandemic and pending the establishment of vaccination campaigns, several non pharmaceutical interventions such as partial and full lockdown, quarantine and measures of physical distancing have been imposed in order to reduce the spread of the disease and to lift the pressure on healthcare system. Mathematical models are important tools for estimating the impact of these interventions, for monitoring the current evolution of the epidemic at a national level and for estimating the potential long-term consequences of relaxation of measures. In this paper, we model the evolution of the covid-19 epidemic in Belgium with a deterministic age-structured extended compartmental model. Our model takes special consideration for nursing homes which are modelled as separate entities from the general population in order to capture the specific delay and dynamics within these entities. The model integrates social contact data and is fitted on hospitalisations data (admission and discharge), on the daily number of covid-19 deaths (with a distinction between general population and nursing homes related deaths) and results from serological studies. The sensitivity analysis of the estimated parameters relies on a Bayesian approach using Markov Chain Monte Carlo methods. We present the situation as in November 2020 with the estimation of some characteristics of the covid-19 deduced from the model. We also present several mid-term and long-term projections based on scenarios of reinforcement or relaxation of social contacts for different general sectors, with a lot of uncertainties remaining.