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

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.

Real-time forecasting of COVID-19-related hospital strain in France using a non-Markovian mechanistic model

“…These models provide us with a mechanistic understanding of the epidemic process and can help to anticipate planned changes such as lockdowns or increases in vaccination coverage. A limitation of compartmental models is that they typically require large, idealised populations for best results [ 13 ] and can have lower predictive performance [ 14 ] depending on the time scale. However, as shown in [ 15 ], a non-Markovian discrete-time compartmental model may have the potential to capture the dynamics up to 5 weeks on average (although this also reflects the epidemiological relevance of the underlying assumptions made).…”

A Novel Computational Instrument Based on a Universal Mixture Density Network with a Gaussian Mixture Model as a Backbone for Predicting COVID-19 Variants’ Distributions

“…As a result, numerous mathematical models have been developed to study the virus's transmission . From a statistical perspective, these models can be classified into deterministic staging or compartmental models (CMs) [1][2][3][4][5][6][7][8][9][10][11] and stochastic models (SMs) [12,13]. In addition, machine learning (ML) [15][16][17][18][19] and neural networks (NNs) [20][21][22][23][24][25][26][27][28] have also been used to create COVID-19 models.…”

Real-time forecasting of COVID-19-related hospital strain in France using a non-Markovian mechanistic model

“…These models provide us with a mechanistic understanding of the epidemic process and can help to anticipate planned changes such as lockdowns or increases in vaccination coverage. A limitation of compartmental models is that they typically require large, idealised populations for best results [10] and can have lower predictive performance [11] depending on the time scale. However, as shown in [12], a non-Markovian discrete-time compartmental model may have the potential to capture the dynamics up to 5 weeks on average (although this also reflects the epidemiological relevance of the underlying assumptions made).…”