Endemic-epidemic models to understand COVID-19 spatio-temporal evolution

Abstract

We propose an endemic-epidemic model: a negative binomial space-time autoregression, which can be employed to monitor the contagion dynamics of the COVID-19 pandemic, both in time and in space. The model is exemplified through an empirical analysis of the provinces of northern Italy, heavily affected by the pandemic and characterized by similar non-pharmaceutical policy interventions.

Keywords: COVID-19; Contagion models; Multivariate statistics; Poisson processes; Spatio-temporal models.

Fig. 1

Parameters to be estimated and their dependency based on the specification (1)–(7).

Fig. 2

(a) Confirmed COVID-19 daily cases in the five regions considered from 25/02/2020 to 21/12/2020. The vertical dotted line splits the training set (until 30/11/2020) and the test set (from 01/12/2020). (b) Weighted undirected graph obtained from the adjacency matrix with entries $o_{i,p}$ for all the provinces.

Fig. 3

(a) Estimated normalized weights $u_d$ for $d=1,\dots ,7$. (b) Observed daily counts (black points) and fitted means split in the epidemic-within (blue), epidemic-between (orange) and endemic (grey) from 25/02/2020 to 30/11/2020 for the twelve most affected provinces. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 4

Province varying random intercepts of the epidemic-within component with 95% confidence interval.

Fig. 5

Province varying random intercepts of the epidemic-between components with 95% confidence interval.

Fig. 6

Observed (black line) and predicted counts for HHH (red dotted line) and for INGARCH (green dotted line) in the test period for the twelve most affected provinces.