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

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.

[1]  G. Roberts,et al.  Bayesian inference for partially observed stochastic epidemics , 1999 .

[2]  Quentin J. Leclerc,et al.  Reconstructing the early global dynamics of under-ascertained COVID-19 cases and infections , 2020, BMC Medicine.

[3]  Christel Faes,et al.  Estimating the generation interval for COVID-19 based on symptom onset data , 2020, medRxiv.

[4]  G. Toraldo,et al.  Tracing day-zero and forecasting the COVID-19 outbreak in Lombardy, Italy: A compartmental modelling and numerical optimization approach , 2020, PloS one.

[5]  Carlos Castillo-Chavez,et al.  Mathematical Models in Epidemiology , 2019, Texts in Applied Mathematics.

[6]  Yang Liu,et al.  Early dynamics of transmission and control of COVID-19: a mathematical modelling study , 2020, The Lancet Infectious Diseases.

[7]  Leila Taghizadeh,et al.  Uncertainty quantification in epidemiological models for the COVID-19 pandemic , 2020, Computers in Biology and Medicine.

[8]  Fabiana Zama,et al.  Monitoring Italian COVID-19 spread by a forced SEIRD model , 2020, PloS one.

[9]  Geoffrey I. Webb,et al.  Predicting the number of reported and unreported cases for the COVID-19 epidemics in China, South Korea, Italy, France, Germany and United Kingdom , 2020, Journal of Theoretical Biology.

[10]  M. Ndeffo-Mbah,et al.  State-level needs for social distancing and contact tracing to contain COVID-19 in the United States , 2020, Nature Human Behaviour.

[11]  Frank Diederich,et al.  Mathematical Epidemiology Of Infectious Diseases Model Building Analysis And Interpretation , 2016 .

[12]  Bernard Moulin,et al.  Analyzing and Modeling Spatial and Temporal Dynamics of Infectious Diseases: Chen/Analyzing , 2014 .

[13]  Jorge Nocedal,et al.  Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization , 1997, TOMS.

[14]  V. Colizza,et al.  Impact of lockdown on COVID-19 epidemic in Île-de-France and possible exit strategies , 2020, BMC Medicine.

[15]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[16]  M. Hernán,et al.  Prevalence of SARS-CoV-2 in Spain (ENE-COVID): a nationwide, population-based seroepidemiological study , 2020, The Lancet.

[17]  Odo Diekmann,et al.  Mathematical Tools for Understanding Infectious Disease Dynamics , 2012 .

[18]  Bernard Moulin,et al.  Introduction to Analyzing and Modeling Spatial and Temporal Dynamics of Infectious Diseases , 2015 .

[19]  Simon Cauchemez,et al.  new approach to characterising infectious disease transmission dynamics from entinel surveillance : Application to the Italian 2009 – 2010 A / H 1 N 1 influenza andemic , 2012 .

[20]  Lucie Abeler-Dörner,et al.  Quantifying SARS-CoV-2 transmission suggests epidemic control with digital contact tracing , 2020, Science.

[21]  J. Ramsay,et al.  Curve registration , 2018, Oxford Handbooks Online.

[22]  D. Cummings,et al.  Age-specific mortality and immunity patterns of SARS-CoV-2 infection in 45 countries , 2020, medRxiv.

[23]  J. Ioannidis,et al.  Visualizing the invisible: The effect of asymptomatic transmission on the outbreak dynamics of COVID-19 , 2020, Computer Methods in Applied Mechanics and Engineering.

[24]  B. Finkenstädt,et al.  Statistical Inference in a Stochastic Epidemic SEIR Model with Control Intervention: Ebola as a Case Study , 2006, Biometrics.

[25]  S. Merler,et al.  Retrospective analysis of the Italian exit strategy from COVID-19 lockdown , 2021, Proceedings of the National Academy of Sciences.

[26]  Alessandro Vespignani,et al.  Prediction and predictability of global epidemics: the role of the airline transportation network , 2005, q-bio/0507029.

[27]  Ralph C. Smith,et al.  Parameter Estimation Using the Python Package pymcmcstat , 2019 .

[28]  Hoon Kim,et al.  Monte Carlo Statistical Methods , 2000, Technometrics.

[29]  Samir Bhatt,et al.  Report 34: COVID-19 infection fatality ratio: estimates from seroprevalence , 2020 .

[30]  Alessandro Vespignani,et al.  Multiscale mobility networks and the spatial spreading of infectious diseases , 2009, Proceedings of the National Academy of Sciences.

[31]  Maia Martcheva,et al.  An Introduction to Mathematical Epidemiology , 2015 .

[32]  Yuan Lou,et al.  Asymptotic Profiles of the Steady States for an SIS Epidemic Patch Model , 2007, SIAM J. Appl. Math..

[33]  HighWire Press.  Proceedings of the Royal Society of London. Series A, Containing papers of a mathematical and physical character , 1934 .

[34]  Chiara Piazzola,et al.  A note on tools for prediction under uncertainty and identifiability of SIR-like dynamical systems for epidemiology. , 2020, Mathematical biosciences.

[35]  A. Rinaldo,et al.  Spread and dynamics of the COVID-19 epidemic in Italy: Effects of emergency containment measures , 2020, Proceedings of the National Academy of Sciences.

[36]  D. Cummings,et al.  Age-specific mortality and immunity patterns of SARS-CoV-2 , 2020, Nature.

[37]  P. Magal,et al.  Predicting the number of reported and unreported cases for the COVID-19 epidemics in China, South Korea, Italy, France, Germany and United Kingdom , 2020, Journal of Theoretical Biology.

[38]  Ruiyun Li,et al.  Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV-2) , 2020, Science.

[39]  Wan-Tong Li,et al.  Dynamics of a nonlocal dispersal SIS epidemic model with Neumann boundary conditions , 2019, Journal of Differential Equations.

[40]  A. Rinaldo,et al.  The geography of COVID-19 spread in Italy and implications for the relaxation of confinement measures , 2020, Nature Communications.

[41]  Philip D. O'Neill,et al.  Mathematical Tools for Understanding Infectious Disease Dynamics by O. Diekmann, H. Heesterbeek and T. Britton Princeton University Press, pp. 516, ISBN 978-0-691-15539-5 , 2013 .

[42]  J. Arino,et al.  A multi-city epidemic model , 2003 .

[43]  A. Rinaldo,et al.  The geography of COVID-19 spread in Italy and implications for the relaxation of confinement measures , 2020, Nature Communications.

[44]  P. Colaneri,et al.  Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy , 2020, Nature Medicine.

[45]  Heikki Haario,et al.  DRAM: Efficient adaptive MCMC , 2006, Stat. Comput..

[46]  Francesco De Lellis,et al.  A network model of Italy shows that intermittent regional strategies can alleviate the COVID-19 epidemic , 2020, Nature Communications.

[47]  S. Bhatt,et al.  Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe , 2020, Nature.

[48]  N. Ferguson,et al.  Role of social networks in shaping disease transmission during a community outbreak of 2009 H1N1 pandemic influenza , 2011, Proceedings of the National Academy of Sciences.

[49]  D. Brockmann,et al.  Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China , 2020, Science.

[50]  P. Klepac,et al.  Early dynamics of transmission and control of COVID-19: a mathematical modelling study , 2020, The Lancet Infectious Diseases.

[51]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..