Intensive care unit occupancy predictions in the COVID-19 pandemic based on age-structured modelling and differential flatness

Abstract

The COVID-19 pandemic confronts governments and their health systems with great challenges for disease management. In many countries, hospitalization and in particular ICU occupancy is the primary measure for policy makers to decide on possible non-pharmaceutical interventions. In this paper a combined methodology for the prediction of COVID-19 case numbers, case-specific hospitalization and ICU admission rates as well as hospital and ICU occupancies is proposed. To this end, we employ differential flatness to provide estimates of the states of an epidemiological compartmental model and estimates of the unknown exogenous inputs driving its nonlinear dynamics. A main advantage of this method is that it requires the reported infection cases as the only data source. As vaccination rates and case-specific ICU rates are both strongly age-dependent, specifically an age-structured compartmental model is proposed to estimate and predict the spread of the epidemic across different age groups. By utilizing these predictions, case-specific hospitalization and case-specific ICU rates are subsequently estimated using deconvolution techniques. In an analysis of various countries we demonstrate how the methodology is able to produce real-time state estimates and hospital/ICU occupancy predictions for several weeks thus providing a sound basis for policy makers.

Toward More Realistic Social Distancing Policies via Advanced Feedback Control

“…This concept [45,46] (see also the books [47][48][49][50]) has given rise, as is commonly known, to numerous concrete applications mainly in engineering (see, e.g., [51] for a recent excellent publication about cranes), but also in other domains (see, e.g., [52] in quantum physics). Also of particular interest here is its use [53] for COVID-19 predictions. Take a flat system with a single control variable u(t) and a flat output variable y(t).…”

Toward more realistic social distancing policies via advanced feedback control

“…It turns out that even simple models help pose important questions about the underlying mechanisms of infection spread and possible means of control of an epidemic. In addition, the rate of infection and other fundamental quantities are difficult, if not impossible, to know precisely (see, e.g., [Havers et al(2020)], [Pérez-Rechel et al(2021)], [Perkins et al(2020)]). This epistemological hindrance to mathematical epidemiology provides further legitimacy for using a parsimonious modeling.…”

“…This concept [Fliess et al(1995)], [Fliess et al(1999)] (see also the books [Sira-Ramírez & Agrawal(2004)], [Lévine(2009)], [Rigatos(2015)], [Rudolph(2021)]) has given rise, as is commonly known, to numerous concrete applications mainly in engineering (see, e.g., [Bonnabel & Clayes(2020)] for a recent excellent 1 CRAN (CNRS, UMR 7039)), Université de Lorraine, BP 239, 54506 Vandoeuvre-lès-Nancy, France; cedric.join@univ-lorraine.f 2 Dipartimento di Matematica e Geoscienze, Università di Trieste, Via Alfonso Valerio 12, 34127 Trieste, Italy; alberto.d'onofrio@units.it 3 LIX (CNRS, UMR 7161), École polytechnique, 91128 Palaiseau, France; Michel.Fliess@polytechnique.edu 4 AL.I.E.N., 7 rue Maurice Barrès, 54330 Vézelise, France; {cedric.join, michel.fliess,}@alien-sas.com publication about cranes), but also in other domains (see, e.g., [Guéry-Odelin et al(2019)] in quantum physics). Also of particular interest here is its use [Hametner et al(2022)] for COVID-19 predictions. Take a flat system with a single control variable u(t) and a flat output variable y(t).…”

“…g ., [Guéry-Odelin et al(2019)] in quantum physics). Also of particular interest here is its use [Hametner et al(2022)] for COVID-19 predictions.…”

Preface to the special issue “Complex dynamics of COVID-19: modeling, prediction and control (part II)”

“…Ghosh et al [ 4 ] investigate the characteristics of a multi-wave SIR model, in which the origin of the multi-wave pattern in the solution of this model is explained, and the features of these pandemic waves in India are explained successfully. Hametner et al [ 5 ] propose a methodology to predict the COVID-19 case numbers, case-specific hospitalization and ICU admission rates as well as hospital and ICU occupancies, and differential flatness is used to provide estimates of the states of an epidemiological compartmental model and estimates of the unknown exogenous inputs driving its nonlinear dynamics. Hoque et al [ 6 ] introduce a SEIATR compartmental model to analyze and predict the COVID-19 outbreak in seriously affected countries in the world including USA, India, Brazil, France, and Russia.…”