SUIHTER : a new mathematical model for COVID-19. Application to the analysis of the second epidemic outbreak in Italy

Abstract

The COVID-19 epidemic is the latest in a long list of pandemics that have affected humankind in the last century. In this paper, we propose a novel mathematical epidemiological model named SUIHTER from the names of the seven compartments that it comprises: susceptible uninfected individuals ( S ), undetected (both asymptomatic and symptomatic) infected ( U ), isolated infected ( I ), hospitalized ( H ), threatened ( T ), extinct ( E ) and recovered ( R ). A suitable parameter calibration that is based on the combined use of the least-squares method and the Markov chain Monte Carlo method is proposed with the aim of reproducing the past history of the epidemic in Italy, which surfaced in late February and is still ongoing to date, and of validating SUIHTER in terms of its predicting capabilities. A distinctive feature of the new model is that it allows a one-to-one calibration strategy between the model compartments and the data that are made available daily by the Italian Civil Protection Department. The new model is then applied to the analysis of the Italian epidemic with emphasis on the second outbreak, which emerged in autumn 2020. In particular, we show that the epidemiological model SUIHTER can be suitably used in a predictive manner to perform scenario analysis at a national level.

Effects of Vaccination Efficacy on Wealth Distribution in Kinetic Epidemic Models

“…We consider the simplified case where , and , for which we obtained the steady distributions in ( 25 ). These values are representative of realistic dynamics during the beginning of the COVID-19 pandemic; see, e.g., [ 6 , 7 , 8 , 39 , 54 ].…”

“…The model can be easily adapted to include disease-related mortality and other compartments of interest in terms of available data, such as records of hospitalized individuals. We refer to [ 3 , 6 , 7 , 42 ] and the references therein for possible developments in these directions. It should be noted that, since we are referring to an advanced epidemic situation in which we assume the existence of a vaccine, the dynamics of unidentified asymptomatic individuals, so significant in the early stages of the COVID-19 pandemic, has become less relevant thanks to mass screening programs.…”

“…A first attempt to understand changes in wealth distribution in the presence of epidemic spread was proposed in [ 1 ] by combining the classical SIR compartmental model of susceptible, infected and recovered individuals [ 2 , 3 ] with the kinetic model of wealth distribution introduced in [ 4 ], and assuming that, due to the presence of the pandemic, individuals in different compartments act differently in the economic process. Although the model was developed in a relatively simplified context, it has provided a general framework for socio-epidemiological modeling that can be easily extended to more complex dynamics, both in terms of economic transactions [ 5 ] and in terms of epidemic interactions [ 6 , 7 ]. We mention in this direction the recent survey reported in [ 8 ] and the seminal approaches proposed in [ 9 , 10 , 11 , 12 ] investigating the economic effects of infectious diseases, as well as the study presented in [ 13 ].…”

Modelling the COVID-19 epidemic and the vaccination campaign in Italy by the SUIHTER model

“…For an overview on recent advances in mathematical epidemiology, computational modelling, physics-based simulation, data science, and machine learning applied to the COVID-19 pandemic, we refer the reader to ( Kuhl, 2021 ). Even limiting the focus to the Italian context, several contributions have been proposed to accurately describe the spatio-temporal spreading of the epidemic in Italy ( Bertuzzo et al, 2020 ; Della Rossa et al, 2020 ; Gatto et al, 2020 ; Giordano et al, 2020 ; Loli Piccolomini & Zama, 2020 ), to forecast its future evolution ( Bartolucci et al, 2021 ; Farcomeni et al, 2021 ; Parolini et al, 2021a ) and to quantify (and possibly optimize) the effects of containing measures, including both pharmaceutical and non-pharmaceutical interventions (NPIs) ( Bonifazi et al, 2021 ; Giordano et al, 2021 ; Marziano et al, 2021 ).…”

“…SUIHTER is an epidemiological model, first introduced in ( Parolini et al, 2021a ), which is designed to conform to the epidemiological data that have been made available by the Italian Authorities since the beginning of the epidemics. The choice of the compartments defining the model has been driven by the assumption that the model should match as close as possible such available data.…”