We recently described a dynamic causal model of a COVID-19 outbreak within a
single region. Here, we combine several of these (epidemic) models to create a
(pandemic) model of viral spread among regions. Our focus is on a second wave
of new cases that may result from loss of immunity--and the exchange of people
between regions--and how mortality rates can be ameliorated under different
strategic responses. In particular, we consider hard or soft social distancing
strategies predicated on national (Federal) or regional (State) estimates of
the prevalence of infection in the population. The modelling is demonstrated
using timeseries of new cases and deaths from the United States to estimate the
parameters of a factorial (compartmental) epidemiological model of each State
and, crucially, coupling between States. Using Bayesian model reduction, we
identify the effective connectivity between States that best explains the
initial phases of the outbreak in the United States. Using the ensuing
posterior parameter estimates, we then evaluate the likely outcomes of
different policies in terms of mortality, working days lost due to lockdown and
demands upon critical care. The provisional results of this modelling suggest
that social distancing and loss of immunity are the two key factors that
underwrite a return to endemic equilibrium.Comment: Technical report: 35 pages, 14 figures, 1 tabl