Model-based assessment of COVID-19 epidemic dynamics by wastewater analysis

in Science of the Total Environment (2022), 827

Continuous surveillance of COVID-19 diffusion remains crucial to control its diffusion and to anticipate infection waves. Detecting viral RNA load in wastewater samples has been suggested as an effective ... [more ▼]

Continuous surveillance of COVID-19 diffusion remains crucial to control its diffusion and to anticipate infection waves. Detecting viral RNA load in wastewater samples has been suggested as an effective approach for epidemic monitoring and the development of an effective warning system. However, its quantitative link to the epidemic status and the stages of outbreak is still elusive. Modelling is thus crucial to address these challenges. In this study, we present a novel mechanistic model-based approach to reconstruct the complete epidemic dynamics from SARS-CoV-2 viral load in wastewater. Our approach integrates noisy wastewater data and daily case numbers into a dynamical epidemiological model. As demonstrated for various regions and sampling protocols, it quantifies the case numbers, provides epidemic indicators and accurately infers future epidemic trends. Following its quantitative analysis, we also provide recommendations for wastewater data standards and for their use as warning indicators against new infection waves. In situations of reduced testing capacity, our modelling approach can enhance the surveillance of wastewater for early epidemic prediction and robust and cost-effective real-time monitoring of local COVID-19 dynamics. [less ▲]

Modelling COVID-19 dynamics and potential for herd immunity by vaccination in Austria, Luxembourg and Sweden

in Journal of Theoretical Biology (2021)

Against the COVID-19 pandemic, non-pharmaceutical interventions have been widely applied and vaccinations have taken off. The upcoming question is how the interplay between vaccinations and social ... [more ▼]

Against the COVID-19 pandemic, non-pharmaceutical interventions have been widely applied and vaccinations have taken off. The upcoming question is how the interplay between vaccinations and social measures will shape infections and hospitalizations. Hence, we extend the Susceptible-Exposed-Infectious-Removed (SEIR) model including these elements. We calibrate it to data of Luxembourg, Austria and Sweden until 15 December 2020. Sweden results having the highest fraction of undetected, Luxembourg of infected and all three being far from herd immunity in December. We quantify the level of social interaction, showing that a level around 1/3 of before the pandemic was still required in December to keep the effective reproduction number Refft below 1, for all three countries. Aiming to vaccinate the whole population within 1 year at constant rate would require on average 1,700 fully vaccinated people/day in Luxembourg, 24,000 in Austria and 28,000 in Sweden, and could lead to herd immunity only by mid summer. Herd immunity might not be reached in 2021 if too slow vaccines rollout speeds are employed. The model thus estimates which vaccination rates are too low to allow reaching herd immunity in 2021, depending on social interactions. Vaccination will considerably, but not immediately, help to curb the infection; thus limiting social interactions remains crucial for the months to come. [less ▲]

Gene regulatory network inference from sparsely sampled noisy data

in Nature Communications (2020), 11

The complexity of biological systems is encoded in gene regulatory networks. Unravelling this intricate web is a fundamental step in understanding the mechanisms of life and eventually developing ... [more ▼]

The complexity of biological systems is encoded in gene regulatory networks. Unravelling this intricate web is a fundamental step in understanding the mechanisms of life and eventually developing efficient therapies to treat and cure diseases. The major obstacle in inferring gene regulatory networks is the lack of data. While time series data are nowadays widely available, they are typically noisy, with low sampling frequency and overall small number of samples. This paper develops a method called BINGO to specifically deal with these issues. Benchmarked with both real and simulated time-series data covering many different gene regulatory networks, BINGO clearly and consistently outperforms state-of-the-art methods. The novelty of BINGO lies in a nonparametric approach featuring statistical sampling of continuous gene expression profiles. BINGO’s superior performance and ease of use, even by non-specialists, make gene regulatory network inference available to any researcher, helping to decipher the complex mechanisms of life. [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 and 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 ▲]

Convergence of discrete time Kalman filter estimate to continuous time estimate

in International Journal of Control (2016), 89(4), 668-679

Composition of passive boundary control systems

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

Interaction of vocal fold and vocal tract oscillations

in Proceedings of the 24th Nordic Seminar on Computational Mechanics (2011)

We study the mechanical feedback coupling between the human vocal folds and vocal tract (VT) by simulating fundamental frequency glides over the lowest VT resonance. In the classical source–filter theory ... [more ▼]

We study the mechanical feedback coupling between the human vocal folds and vocal tract (VT) by simulating fundamental frequency glides over the lowest VT resonance. In the classical source–filter theory of speech production, the vocal folds produce a signal which is filtered by the resonator, vocal tract without any feedback. We have developed a computational model of the vocal folds and the VT that also includes a counter pressure from the VT to the vocal folds. This coupling gives rise to new computational observations (such as modal locking) that can be established experimentally. [less ▲]