  Spatio-temporal models for infection counts generally follow themes of the
broader disease mapping literature, but may need to address specific features
of spatio-temporal infection data including considerable time fluctuations
(with epidemic phases) and spatial diffusion. Low order autoregression is a
feature of several recent spatio-temporal studies of infection data, possibly
with lags on both within area infections and on infections in adjacent areas.
Many epidemic time series show a period of relatively stable infection levels
(possibly characterized as endemicity), followed by a sudden sharp phase of
increasing infection levels. After the epidemic peak there is a period of
descending rates and return to stability. Hence one may seek to adapt the
autoregressive scheme to these pronounced fluctuations, with temporary
departures from stationarity, but returning to stationarity as rates descend
and infections resume endemic levels. We consider a mixture link model for
infection counts that allows adaptivity to both explosive phases and static
endemicity. Two case study applications involve COVID area-time data, one for
32 London boroughs since the start of the COVID epidemic, the other focusing on
the epidemic phase in 144 area of South East England associated with the Delta
variant.
