The evolving SARS-CoV-2 epidemic in Africa: Insights from rapidly expanding genomic surveillance

INTRODUCTION Investment in Africa over the past year with regard to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) sequencing has led to a massive increase in the number of sequences, which, to date, exceeds 100,000 sequences generated to track the pandemic on the continent. These sequences have profoundly affected how public health officials in Africa have navigated the COVID-19 pandemic. RATIONALE We demonstrate how the first 100,000 SARS-CoV-2 sequences from Africa have helped monitor the epidemic on the continent, how genomic surveillance expanded over the course of the pandemic, and how we adapted our sequencing methods to deal with an evolving virus. Finally, we also examine how viral lineages have spread across the continent in a phylogeographic framework to gain insights into the underlying temporal and spatial transmission dynamics for several variants of concern (VOCs). RESULTS Our results indicate that the number of countries in Africa that can sequence the virus within their own borders is growing and that this is coupled with a shorter turnaround time from the time of sampling to sequence submission. Ongoing evolution necessitated the continual updating of primer sets, and, as a result, eight primer sets were designed in tandem with viral evolution and used to ensure effective sequencing of the virus. The pandemic unfolded through multiple waves of infection that were each driven by distinct genetic lineages, with B.1-like ancestral strains associated with the first pandemic wave of infections in 2020. Successive waves on the continent were fueled by different VOCs, with Alpha and Beta cocirculating in distinct spatial patterns during the second wave and Delta and Omicron affecting the whole continent during the third and fourth waves, respectively. Phylogeographic reconstruction points toward distinct differences in viral importation and exportation patterns associated with the Alpha, Beta, Delta, and Omicron variants and subvariants, when considering both Africa versus the rest of the world and viral dissemination within the continent. Our epidemiological and phylogenetic inferences therefore underscore the heterogeneous nature of the pandemic on the continent and highlight key insights and challenges, for instance, recognizing the limitations of low testing proportions. We also highlight the early warning capacity that genomic surveillance in Africa has had for the rest of the world with the detection of new lineages and variants, the most recent being the characterization of various Omicron subvariants. CONCLUSION Sustained investment for diagnostics and genomic surveillance in Africa is needed as the virus continues to evolve. This is important not only to help combat SARS-CoV-2 on the continent but also because it can be used as a platform to help address the many emerging and reemerging infectious disease threats in Africa. In particular, capacity building for local sequencing within countries or within the continent should be prioritized because this is generally associated with shorter turnaround times, providing the most benefit to local public health authorities tasked with pandemic response and mitigation and allowing for the fastest reaction to localized outbreaks. These investments are crucial for pandemic preparedness and response and will serve the health of the continent well into the 21st century

Reduced order modelling for efficient prediction of the dynamics of mistuned bladed disks

The unavoidable existence of small differences between nominally identical sectors of bladed disks, called mistuning, can have an important impact on the dynamic behaviour of these structures. In particular, this has the potential to lead to responses qualitatively different from that of an ideal cyclic, tuned structure and, in turn, to significantly shorter life spans. Study of mistuning as a random phenomenon requires statistical analysis of a large number of mistuning patterns. This computational task is expensive especially when high-fidelity finite element models are used. This research is concerned with the development of reduced order computational modelling techniques for the dynamic analysis of mistuned bladed disks. These techniques combine accuracy and computational efficiency for a reliable statistical assessment of the effects of mistuning on the dynamics of such systems. For free vibration, the nominal assessment of the effects of mistuning on the dynamics of such systems. For free vibration, the nominal periodicity is exploited, leading to an approximation that greatly reduces the order of the original model. The natural frequencies and mode shapes for a passband are found by treating the unknown complex amplitudes between the nominally identical sectors as the generalized co-ordinates of the problem. In spite of a very large reduction in the computational effort, the results obtained are very accurate both for frequencies and mode shapes even when strong mode localization is observed. To test the perfor4mance of the proposed approximation further, a situation where two passbands are brought close to each other is also considered. This method is general in its formulation and has the potential of being used for complex geometries. It is also extended to the frequency response problem. The great advantage is that the statistics of ‘blades’ forced responses can be numerically generated at a cost of a single degree-of-freedom per blade/disk sector model. Furthermore, a stochastic reduced basis approach is developed for the approximation of these statistics. This approach allows for a complete stochastic analysis of the effects of mistuning. The system response is represented using a linear combination of complex stochastic basis vectors with undetermined coefficients. The terms of the preconditioned stochastic Krylov subspace are used as basis vectors. Two variants of the stochastic Bubnov-Galerkin scheme are employed for computing the undetermined terms in the reduced basis representation. Explicit expressions for the response quantities are then derived in terms of the system random parameters. This allows for the possibility of efficiently computing the response statistics in the post-processing stage. This novel approach can be applied either on the original model in the physical domain or on a reduced model in the modal domain as a secondary reduction technique. The accuracy of the response statistical moments computed using this approach can be orders of magnitude better than classical perturbation methods. Finally, component mode synthesis or substructuring and probabilistic methods are combined to generate reduced order models. The Craig-Bampton reduction procedure is applied while using stochastic component modes instead of deterministic modes. An additional calculation of sensitivities of fixed interface modes, constraint modes and substructure-matrices is required with respect to the physical random variables. In the case of turbomachinery mistuned bladed disks composed of nearly identical substructures, the sensitivity analysis can be targeted to only one substructure. One great advantage is that the physical variations can be used as input in the reduced order model. This novel approach allows for an efficient computation of the statistical characteristics of responses and a complete stochastic analysis of the effects of mistuning.<br/

Efficient prediction of the forced response statistics of mistuned bladed discs

This paper presents two efficient reduced-order modelling techniques for predicting the forced response statistics of bladed disc assemblies. First, the formulation presented in (1) is extended to the forced response problem. Component modes for a blade-disc sector are used as basis vectors, leading to a reduced model of the same size as the number of sectors and allowing for pass-band calculations. For each realization of the random system parameters, a reduced system of equations is solved to compute the displacement vector for each frequency band of interest. Statistics of responses at each frequency point can be therefore estimated by performing Monte Carlo Simulations of cost comparable to single degree-of-freedom mass-spring systems. Second, a stochastic reduced basis approach is applied to the mistuning analysis problem. Here, the system response in the frequency domain is represented using a linear combination of complex stochastic basis vectors which span the preconditioned stochastic Krylov Subspace (2,3). Orthogonal stochastic projection schemes are employed for computing the undetermined coefficients in the stochastic reduced basis representation. These schemes lead to explicit expressions for the response to be obtained, thereby allowing the efficient computation of the response statistics

Statistical investigation of the free vibration mistuned blade system

A statistical investigation of the effects of uncertainty in root fixity on the free vibration of turbine blades is made. Emphasis is particularly placed on the statistical properties of the random eigenvalues and essentially on their standard deviations. These are evaluated using the direct product technique between matrices [1] and validated by Monte Carlo SImulations (MCS). The studied system is a simplified model of a shrouded blade assembly under the conditions of weak interblade coupling. It essentially consists of a cyclic chain of continuous beams with identical properties, fixed at one end via rotational springs with random stiffnesses representing the uncertain roots stiffnesses and coupled via linear springs at their tips. Finite Element Method is used as a discretization technique to obtain the equations of motion of the tuned and mistuned systems and the corresponding random eigenvalue problem.Numerical simulations show that small differences between the rotational springs stiffnesses spoilt the natural frequencies that were in pairs, increase the width of each frequency-cluster and strongly localizes the vibration around one blade. This strong localization has been shown to occur in a chain of single-degree-of-freedom, nearly identical, coupled oscillators if the coupling frequency between the subsystems is of order of, or smaller than the spread in the natural frequencies [2]However, for the multi-degree-of-freedom and randomly mistuned system considered her, multiple realizations are required to capture the behaviour of the eigenvalues appearing in frequency-clusters. It is found that for each frequency-cluster, when the standard deviations of the eigenvalues are plotted against the mode number, they form a U-shaped curve. For the particular case when the coupling frequency line crosses a curve, this essentially shows that the vibration localization is stronger at the first and last modes than at the mid frequencies, which belong to one passband in the tuned system