  The evolution of the COVID-19 epidemic has been accompanied by accumulating
evidence on the underlying epidemiological parameters. Hence there is potential
for models providing mid-term forecasts of the epidemic trajectory using such
information. The effectiveness of lockdown interventions can also be assessed
by modelling later epidemic stages, possibly using a multiphase epidemic model.
Commonly applied methods to analyze epidemic trajectories include
phenomenological growth models (e.g. the Richards), and variants of the
susceptible-infected-recovered (SIR) compartment model. Here we focus on a
practical forecasting approach, applied to interim UK COVID data, using a
bivariate Reynolds model (cases and deaths). We show the utility of informative
priors in developing and estimating the model, and compare error densities
(Poisson-gamma, Poisson-lognormal, Poisson-logStudent) for overdispersed data
on new cases and deaths. We use cross-validation to assess medium term
forecasts. We also consider the longer term post-lockdown epidemic profile to
assess epidemic containment, using a two phase model. Fit to mid-epidemic data
shows better fit to training data and better cross validation performance for a
Poisson-logStudent model. Estimation of longer term epidemic data after
lockdown relaxation, characterised by protracted slow downturn and then upturn
in cases, casts doubt on effective containment. Many applications of
phenomenological models have been to complete epidemics. However, evaluation of
such models based simply on their fit to observed data may give only a partial
picture, and cross-validation against actual trends is also useful. Similarly,
it may be preferable to model incidence rather than cumulative data, though
this raises questions about suitable error densities for modelling often
erratic fluctuations. Hence there may be utility in evaluating alternative
error assumptions.
