Spatial modelling of COVID-19 incident cases using Richards' curve: an application to the Italian regions

TL;DR

This paper develops a Bayesian spatial-temporal model using Richards' curve to analyze COVID-19 cases in Italian regions, capturing dependence across regions and over time, and providing improved predictions over independent models.

Contribution

It introduces a novel extended logistic growth model with spatial and temporal dependence for COVID-19 data, estimated within a Bayesian framework using Stan.

Findings

Significant spatial and temporal dependence in COVID-19 waves in Italy.

The model improves prediction accuracy over independent region models.

Spatial dependence persisted despite restrictive measures.

Abstract

We introduce an extended generalised logistic growth model for discrete outcomes, in which a network structure can be specified to deal with spatial dependence and time dependence is dealt with using an Auto-Regressive approach. A major challenge concerns the specification of the network structure, crucial to consistently estimate the canonical parameters of the generalised logistic curve, e.g. peak time and height. Parameters are estimated under the Bayesian framework, using the {\texttt{ Stan}} probabilistic programming language. The proposed approach is motivated by the analysis of the first and second wave of COVID-19 in Italy, i.e. from February 2020 to July 2020 and from July 2020 to December 2020, respectively. We analyse data at the regional level and, interestingly enough, prove that substantial spatial and temporal dependence occurred in both waves, although strong restrictive measures were implemented during the first wave. Accurate predictions are obtained, improving those of the model where independence across regions is assumed.