Spatio-temporal models need to address specific features of spatio-temporal infection data, such as periods of stable infection levels (endemicity), followed by epidemic phases, as well as infection spread from neighbouring areas. In this paper, we consider a mixture-link model for infection counts that allows alternation between epidemic phases (possibly multiple) and stable endemicity, with higher AR1 coefficients in epidemic phases. This is a form of regime-switching, allowing for non-stationarity in infection levels. We adopt a generalised Poisson model appropriate to the infection count data and avoid transformations (e.g., differencing) to alternative metrics, which have been adopted in many studies. We allow for neighbourhood spillover in infection, which is also governed by adaptive regime-switching. Compared to existing models, the observational (in-sample) model is expected to better reflect the balance between epidemic and endemic tendencies, and short-term extrapolations are likely to be improved. Two case study applications involve COVID area-time data, one for 32 London boroughs (and 96 weeks) since the start of the COVID epidemic, the other for a shorter time span focusing on the epidemic phase in 144 areas of Southeast England associated with the Alpha variant. In both applications, the proposed methods produce a better in-sample fit and out-of-sample short term predictions. The spatial dynamic implications are highlighted in the case studies.
Keywords: autoregressive; endemic; epidemic; regime-switching; spatio-temporal; spillover.