Stages of COVID-19 pandemic and paths to herd immunity by vaccination: dynamical model comparing Austria, Luxembourg and Sweden

E-print/Working paper (2021)

Background. Worldwide more than 72 million people have been infected and 1.6 million died with SARS-CoV-2 by 15th December 2020. Non-pharmaceutical interventions which decrease social interaction have ... [more ▼]

Background. Worldwide more than 72 million people have been infected and 1.6 million died with SARS-CoV-2 by 15th December 2020. Non-pharmaceutical interventions which decrease social interaction have been implemented to reduce the spread of SARS-CoV-2 and to mitigate stress on healthcare systems and prevent deaths. The pandemic has been tackled with disparate strategies by distinct countries resulting in different epidemic dynamics. However, with vaccines now becoming available, the current urgent open question is how the interplay between vaccination strategies and social interaction will shape the pandemic in the next months. Methods. To address this question, we developed an extended Susceptible-Exposed-Infectious-Removed (SEIR) model including social interaction, undetected cases and the progression of patients trough hospitals, intensive care units (ICUs) and death. We calibrated our model to data of Luxembourg, Austria and Sweden, until 15th December 2020. We incorporated the effect of vaccination to investigate under which conditions herd immunity would be achievable in 2021. Results. The model reveals that Sweden has the highest fraction of undetected cases, Luxembourg displays the highest fraction of infected population, and all three countries are far from herd immunity as of December 2020. The model quantifies the level of social interactions, and allows to assess the level which would keep Reff(t) below 1. In December 2020, this level is around 1/3 of what it was before the pandemic for all the three countries. The model allows to estimate the vaccination rate needed for herd immunity and shows that 2700 vaccinations/day are needed in Luxembourg to reach it by mid of April and 45,000 for Austria and Sweden. The model estimates that vaccinating the whole country’s population within 1 year could lead to herd immunity by July in Luxembourg and by August in Austria and Sweden. Conclusion. The model allows to shed light on the dynamics of the epidemics in different waves and countries. Our results emphasize that vaccination will help considerably but not immediately and therefore social measures will remain important for several months before they can be fully alleviated. [less ▲]

COVID-19 Crisis Management in Luxembourg: Insights from an Epidemionomic Approach

E-print/Working paper (2020)

We develop an epidemionomic model that jointly analyzes the health and economic responses to the COVID-19 crisis and to the related containment and public health policy measures implemented in Luxembourg ... [more ▼]

We develop an epidemionomic model that jointly analyzes the health and economic responses to the COVID-19 crisis and to the related containment and public health policy measures implemented in Luxembourg and in the Greater Region. The model has a weekly structure and covers the whole year 2020. With a limited number of parameters, the model is calibrated to depict the pre-crisis evolution of the Luxembourg economy, and to match post-lockdown leading economic indicators and industry-specific infection curves. The nowcasting part of our analysis reveals that each week of lockdown reduces national output by about 28% (and annual GDP by 0.54%). A first peak of the infection curve was observed at the very beginning of April. If the lockdown measures had been permanent, annual GDP would have decreased by 22% in 2020, the number of COVID-19 cases would have reached zero around mid-June, and the proportion of recovered people would have reached 1.4% of the population. In an economy heavily relying on skill-intensive services, we show that the role of teleworking has been instrumental to limiting the weekly economic output loss (almost by one half) and the propagation of the virus. In the forecasting part of the analysis, we quantify the epidemiological and economic responses to gradual deconfinement measures under various public health scenarios. If the post-lockdown transmission rates could be kept constant throughout the deconfinement period, restarting all sectors would have huge effects on the economy (limiting the annual GDP loss to about 7%) and no effect on the aggregate infection curve. While it is a good time for lifting containment measures, there is also a risk that increasing the density of employees at the workplace and resuming social activities would induce a rebound in the infection curve. Preventing such a relapse is possible with PCR testing of both national and cross-border workers, and with accompanying measures such as (i) maintaining teleworking practices, (ii) reopening hotels, restaurants and cafes at half of their full capacity or with equivalent physical distancing measures and last but not least, (iii) sustaining distancing measures in social activities. Overall, in our worst-case scenario, combining bi-monthly testing with contact tracing and quarantining measures appear to be a suficient (perhaps not necessary) policy option in the aftermath of the deconfinement plan. [less ▲]

Linear system identification from ensemble snapshot observations

in Proceedings of the IEEE Conference on Decision and Control (2019, December)

Developments in transcriptomics techniques have caused a large demand in tailored computational methods for modelling gene expression dynamics from experimental data. Recently, so-called single-cell ... [more ▼]

Developments in transcriptomics techniques have caused a large demand in tailored computational methods for modelling gene expression dynamics from experimental data. Recently, so-called single-cell experiments have revolutionised genetic studies. These experiments yield gene expression data in single cell resolution for a large number of cells at a time. However, the cells are destroyed in the measurement process, and so the data consist of snapshots of an ensemble evolving over time, instead of time series. The problem studied in this article is how such data can be used in modelling gene regulatory dynamics. Two different paradigms are studied for linear system identification. The first is based on tracking the evolution of the distribution of cells over time. The second is based on the so-called pseudotime concept, identifying a common trajectory through the state space, along which cells propagate with different rates. Therefore, at any given time, the population contains cells in different stages of the trajectory. Resulting methods are compared in numerical experiments. [less ▲]

Convergence of discrete-time Kalman filter estimate to continuous-time estimate for systems with unbounded observation

in Mathematics of Control, Signals & Systems (2018), 30(3), 9

In this article, we complement recent results on the convergence of the state estimate obtained by applying the discrete-time Kalman filter on a time-sampled continuous-time system. As the temporal ... [more ▼]

In this article, we complement recent results on the convergence of the state estimate obtained by applying the discrete-time Kalman filter on a time-sampled continuous-time system. As the temporal discretization is re fined, the estimate converges to the continuous-time estimate given by the Kalman-Bucy fi lter. We shall give bounds for the convergence rates for the variance of the discrepancy between these two estimates. The contribution of this article is to generalize the convergence results to systems with unbounded observation operators under di fferent sets of assumptions, including systems with diagonalizable generators, systems with admissible observation operators, and systems with analytic semigroups. The proofs are based on applying the discrete-time Kalman fi lter on a dense, numerable subset on the time interval [0,T] and bounding the increments obtained. These bounds are obtained by studying the regularity of the underlying semigroup and the noise-free output. [less ▲]

Modal Locking Between Vocal Fold Oscillations and Vocal Tract Acoustics

in Acta Acustica United with Acustica (2018), 104(2), 323-337

During voiced speech, vocal folds interact with the vocal tract acoustics. The resulting glottal source–resonator coupling has been observed using mathematical and physical models as well as in in vivo ... [more ▼]

During voiced speech, vocal folds interact with the vocal tract acoustics. The resulting glottal source–resonator coupling has been observed using mathematical and physical models as well as in in vivo phonation. We propose a computational time-domain model of the full speech apparatus that contains a feedback mechanism from the vocal tract acoustics to the vocal fold oscillations. It is based on numerical solution of ordinary and partial differential equations defined on vocal tract geometries that have been obtained by magnetic resonance imaging. The model is used to simulate rising and falling pitch glides of [α, i] in the fundamental frequency (fo ) interval [145 Hz, 315 Hz]. The interval contains the first vocal tract resonance fR 1 and the first formant F 1 of [i] as well as the fractions of the first resonance fR 1 /5, fR 1 /4, and fR 1 /3 of [α]. The glide simulations reveal a locking pattern in the fo trajectory approximately at fR 1 of [i]. The resonance fractions of [α] produce perturbations in the pressure signal at the lips but no locking. [less ▲]

Iterative observer-based state and parameter estimation for linear systems

in ESAIM: Control, Optimisation and Calculus of Variations (2018), 24(1), 265-288

We propose an iterative method for joint state and parameter estimation using measurements on a time interval [0,T] for systems that are backward output stabilizable. Since this time interval is fixed ... [more ▼]

We propose an iterative method for joint state and parameter estimation using measurements on a time interval [0,T] for systems that are backward output stabilizable. Since this time interval is fixed, errors in initial state may have a big impact on the parameter estimate. We propose to use the back and forth nudging (BFN) method for estimating the system’s initial state and a Gauss–Newton step between BFN iterations for estimating the system parameters. Taking advantage of results on the optimality of the BFN method, we show that for systems with skew-adjoint generators, the initial state and parameter estimate minimizing an output error cost functional is an attractive fixed point for the proposed method. We treat both linear source estimation and bilinear parameter estimation problems. [less ▲]

Output error minimizing back and forth nudging method for initial state recovery

in Systems & Control Letters (2016), 94

Composition of passive boundary control systems

in Mathematical Control and Related Fields (2013), 3(1), 1-19

Wave propagation in networks: a system theoretic approach

in Proceedings of the 18th World Congress of the IFAC (2011)