Limits of Compartmental Models and New Opportunities for Machine Learning: A Case Study to Forecast the Second Wave of COVID-19 Hospitalizations in Lombardy, Italy

Andrea Gatto,Valeria Aloisi,Francesco Donato,Francesco Immorlano,Gabriele Accarino,Giovanni Aloisio

doi:10.3390/informatics8030057

Abstract

Compartmental models have long been used in epidemiological studies for predicting disease spread. However, a major issue when using compartmental mathematical models concerns the time-invariant formulation of hyper-parameters that prevent the model from following the evolution over time of the epidemiological phenomenon under investigation. In order to cope with this problem, the present work suggests an alternative hybrid approach based on Machine Learning that avoids recalculation of hyper-parameters and only uses an initial set. This study shows that the proposed hybrid approach makes it possible to correct the expected loss of accuracy observed in the compartmental model when the considered time horizon increases. As a case study, a basic compartmental model has been designed and tested to forecast COVID-19 hospitalizations during the first and the second pandemic waves in Lombardy, Italy. The model is based on an extended formulation of the contact function that allows modelling of the trend of personal contacts throughout the reference period. Moreover, the scenario analysis proposed in this work can help policy-makers select the most appropriate containment measures to reduce hospitalizations and relieve pressure on the health system, but also to limit any negative impact on the economic and social systems.

Highlights

This study shows that the proposed hybrid approach makes it possible to correct the expected loss of accuracy observed in the compartmental model when the considered time horizon increases
In early December 2019, the first COronaVIrus Disease-2019 (COVID-19) case was identified in Wuhan, China [1], which started a pandemic that spread across the globe in just a few months [2]
Kucharski and colleagues [13] conducted a mathematical study based on a stochastic SEIR model, with the goal of modelling the early dynamics of COVID-19 pandemic transmission in Wuhan, considering the impact of travelling on the virus spread outside Wuhan

Summary

Introduction

In early December 2019, the first COronaVIrus Disease-2019 (COVID-19) case was identified in Wuhan, China [1], which started a pandemic that spread across the globe in just a few months [2]. A major issue when using compartmental mathematical models relates to the gradual loss of accuracy coming from the time-invariant formulation of hyper-parameters, which prevent the model from following the evolution over time of the epidemiological phenomenon under investigation. Such hyper-parameters are generally calculated on the basis of appropriate estimation algorithms (e.g., MCMC, Maximum Likelihood) that do not provide time-variant formulations though. The developed HSM has been used here to produce accurate predictions about COVID-19 hospitalizations for the second epidemic wave, to simulate different scenarios based on different containment measures and to assess the impact of such measures on the epidemiological curve, using the HSM framework

Population and Data Sources

The Basic SEIR Model

The Hybrid SEIR Model

The Daily Reproduction Number Estimation

Results

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