  We introduce a Bayesian sequential data assimilation method for COVID-19
forecasting. It is assumed that suitable transmission, epidemic and observation
models are available and previously validated and the transmission and epidemic
models are coded into a dynamical system. The observation model depends on the
dynamical system state variables and parameters, and is cast as a likelihood
function. We elicit prior distributions of the effective population size, the
dynamical system initial conditions and infectious contact rate, and use Markov
Chain Monte Carlo sampling to make inference and prediction of quantities of
interest (QoI) at the onset of the epidemic outbreak. The forecast is
sequentially updated over a sliding window of epidemic records as new data
becomes available. Prior distributions for the state variables at the new
forecasting time are assembled using the dynamical system, calibrated for the
previous forecast. Moreover, changes in the contact rate and effective
population size are naturally introduced through auto-regressive models on the
corresponding parameters. We show our forecasting method's performance using a
SEIR type model and COVID-19 data from several Mexican localities.
