A mathematical model to assess the effectiveness of test-trace-isolate-and-quarantine under limited capacities.

Diagnostic testing followed by isolation of identified cases with subsequent tracing and quarantine of close contacts-often referred to as test-trace-isolate-and-quarantine (TTIQ) strategy-is one of the cornerstone measures of infectious disease control. The COVID-19 pandemic has highlighted that an appropriate response to outbreaks of infectious diseases requires a firm understanding of the effectiveness of such containment strategies. To this end, mathematical models provide a promising tool. In this work, we present a delay differential equation model of TTIQ interventions for infectious disease control. Our model incorporates the assumption of limited TTIQ capacities, providing insights into the reduced effectiveness of testing and tracing in high prevalence scenarios. In addition, we account for potential transmission during the early phase of an infection, including presymptomatic transmission, which may be particularly adverse to a TTIQ based control. Our numerical experiments inspired by the early spread of COVID-19 in Germany demonstrate the effectiveness of TTIQ in a scenario where immunity within the population is low and pharmaceutical interventions are absent, which is representative of a typical situation during the (re-)emergence of infectious diseases for which therapeutic drugs or vaccines are not yet available. Stability and sensitivity analyses reveal both disease-dependent and disease-independent factors that impede or enhance the success of TTIQ. Studying the diminishing impact of TTIQ along simulations of an epidemic wave, we highlight consequences for intervention strategies.

Predictive performance of multi-model ensemble forecasts of COVID-19 across European nations.

Background: Short-term forecasts of infectious disease burden can contribute to situational awareness and aid capacity planning. Based on best practice in other fields and recent insights in infectious disease epidemiology, one can maximise the predictive performance of such forecasts if multiple models are combined into an ensemble. Here, we report on the performance of ensembles in predicting COVID-19 cases and deaths across Europe between 08 March 2021 and 07 March 2022. Methods: We used open-source tools to develop a public European COVID-19 Forecast Hub. We invited groups globally to contribute weekly forecasts for COVID-19 cases and deaths reported by a standardised source for 32 countries over the next 1-4 weeks. Teams submitted forecasts from March 2021 using standardised quantiles of the predictive distribution. Each week we created an ensemble forecast, where each predictive quantile was calculated as the equally-weighted average (initially the mean and then from 26th July the median) of all individual models' predictive quantiles. We measured the performance of each model using the relative Weighted Interval Score (WIS), comparing models' forecast accuracy relative to all other models. We retrospectively explored alternative methods for ensemble forecasts, including weighted averages based on models' past predictive performance. Results: Over 52 weeks, we collected forecasts from 48 unique models. We evaluated 29 models' forecast scores in comparison to the ensemble model. We found a weekly ensemble had a consistently strong performance across countries over time. Across all horizons and locations, the ensemble performed better on relative WIS than 83% of participating models' forecasts of incident cases (with a total N=886 predictions from 23 unique models), and 91% of participating models' forecasts of deaths (N=763 predictions from 20 models). Across a 1-4 week time horizon, ensemble performance declined with longer forecast periods when forecasting cases, but remained stable over 4 weeks for incident death forecasts. In every forecast across 32 countries, the ensemble outperformed most contributing models when forecasting either cases or deaths, frequently outperforming all of its individual component models. Among several choices of ensemble methods we found that the most influential and best choice was to use a median average of models instead of using the mean, regardless of methods of weighting component forecast models. Conclusions: Our results support the use of combining forecasts from individual models into an ensemble in order to improve predictive performance across epidemiological targets and populations during infectious disease epidemics. Our findings further suggest that median ensemble methods yield better predictive performance more than ones based on means. Our findings also highlight that forecast consumers should place more weight on incident death forecasts than incident case forecasts at forecast horizons greater than 2 weeks. Funding: AA, BH, BL, LWa, MMa, PP, SV funded by National Institutes of Health (NIH) Grant 1R01GM109718, NSF BIG DATA Grant IIS-1633028, NSF Grant No.: OAC-1916805, NSF Expeditions in Computing Grant CCF-1918656, CCF-1917819, NSF RAPID CNS-2028004, NSF RAPID OAC-2027541, US Centers for Disease Control and Prevention 75D30119C05935, a grant from Google, University of Virginia Strategic Investment Fund award number SIF160, Defense Threat Reduction Agency (DTRA) under Contract No. HDTRA1-19-D-0007, and respectively Virginia Dept of Health Grant VDH-21-501-0141, VDH-21-501-0143, VDH-21-501-0147, VDH-21-501-0145, VDH-21-501-0146, VDH-21-501-0142, VDH-21-501-0148. AF, AMa, GL funded by SMIGE - Modelli statistici inferenziali per governare l'epidemia, FISR 2020-Covid-19 I Fase, FISR2020IP-00156, Codice Progetto: PRJ-0695. AM, BK, FD, FR, JK, JN, JZ, KN, MG, MR, MS, RB funded by Ministry of Science and Higher Education of Poland with grant 28/WFSN/2021 to the University of Warsaw. BRe, CPe, JLAz funded by Ministerio de Sanidad/ISCIII. BT, PG funded by PERISCOPE European H2020 project, contract number 101016233. CP, DL, EA, MC, SA funded by European Commission - Directorate-General for Communications Networks, Content and Technology through the contract LC-01485746, and Ministerio de Ciencia, Innovacion y Universidades and FEDER, with the project PGC2018-095456-B-I00. DE., MGu funded by Spanish Ministry of Health / REACT-UE (FEDER). DO, GF, IMi, LC funded by Laboratory Directed Research and Development program of Los Alamos National Laboratory (LANL) under project number 20200700ER. DS, ELR, GG, NGR, NW, YW funded by National Institutes of General Medical Sciences (R35GM119582; the content is solely the responsibility of the authors and does not necessarily represent the official views of NIGMS or the National Institutes of Health). FB, FP funded by InPresa, Lombardy Region, Italy. HG, KS funded by European Centre for Disease Prevention and Control. IV funded by Agencia de Qualitat i Avaluacio Sanitaries de Catalunya (AQuAS) through contract 2021-021OE. JDe, SMo, VP funded by Netzwerk Universitatsmedizin (NUM) project egePan (01KX2021). JPB, SH, TH funded by Federal Ministry of Education and Research (BMBF; grant 05M18SIA). KH, MSc, YKh funded by Project SaxoCOV, funded by the German Free State of Saxony. Presentation of data, model results and simulations also funded by the NFDI4Health Task Force COVID-19 (https://www.nfdi4health.de/task-force-covid-19-2) within the framework of a DFG-project (LO-342/17-1). LP, VE funded by Mathematical and Statistical modelling project (MUNI/A/1615/2020), Online platform for real-time monitoring, analysis and management of epidemic situations (MUNI/11/02202001/2020); VE also supported by RECETOX research infrastructure (Ministry of Education, Youth and Sports of the Czech Republic: LM2018121), the CETOCOEN EXCELLENCE (CZ.02.1.01/0.0/0.0/17-043/0009632), RECETOX RI project (CZ.02.1.01/0.0/0.0/16-013/0001761). NIB funded by Health Protection Research Unit (grant code NIHR200908). SAb, SF funded by Wellcome Trust (210758/Z/18/Z).

National and subnational short-term forecasting of COVID-19 in Germany and Poland during early 2021.

BACKGROUND: During the COVID-19 pandemic there has been a strong interest in forecasts of the short-term development of epidemiological indicators to inform decision makers. In this study we evaluate probabilistic real-time predictions of confirmed cases and deaths from COVID-19 in Germany and Poland for the period from January through April 2021. METHODS: We evaluate probabilistic real-time predictions of confirmed cases and deaths from COVID-19 in Germany and Poland. These were issued by 15 different forecasting models, run by independent research teams. Moreover, we study the performance of combined ensemble forecasts. Evaluation of probabilistic forecasts is based on proper scoring rules, along with interval coverage proportions to assess calibration. The presented work is part of a pre-registered evaluation study. RESULTS: We find that many, though not all, models outperform a simple baseline model up to four weeks ahead for the considered targets. Ensemble methods show very good relative performance. The addressed time period is characterized by rather stable non-pharmaceutical interventions in both countries, making short-term predictions more straightforward than in previous periods. However, major trend changes in reported cases, like the rebound in cases due to the rise of the B.1.1.7 (Alpha) variant in March 2021, prove challenging to predict. CONCLUSIONS: Multi-model approaches can help to improve the performance of epidemiological forecasts. However, while death numbers can be predicted with some success based on current case and hospitalization data, predictability of case numbers remains low beyond quite short time horizons. Additional data sources including sequencing and mobility data, which were not extensively used in the present study, may help to improve performance.

We compare forecasts of weekly case and death numbers for COVID-19 in Germany and Poland based on 15 different modelling approaches. These cover the period from January to April 2021 and address numbers of cases and deaths one and two weeks into the future, along with the respective uncertainties. We find that combining different forecasts into one forecast can enable better predictions. However, case numbers over longer periods were challenging to predict. Additional data sources, such as information about different versions of the SARS-CoV-2 virus present in the population, might improve forecasts in the future.

Compliance with NPIs and possible deleterious effects on mitigation of an epidemic outbreak.

The first attempt to control and mitigate an epidemic outbreak caused by a previously unknown virus occurs primarily via non-pharmaceutical interventions (NPIs). In case of the SARS-CoV-2 virus, which since the early days of 2020 caused the COVID-19 pandemic, NPIs aimed at reducing transmission-enabling contacts between individuals. The effectiveness of contact reduction measures directly correlates with the number of individuals adhering to such measures. Here, we illustrate by means of a very simple compartmental model how partial noncompliance with NPIs can prevent these from stopping the spread of an epidemic.

Germany's next shutdown-Possible scenarios and outcomes.

With the rapid increase of reported COVID-19 cases, German policymakers announced a 4-week "shutdown light" starting on November 2, 2020. Applying mathematical models, possible scenarios for the evolution of the outbreak in Germany are simulated. The results indicate that independent of the effectiveness of the current restrictive measures they might not be sufficient to mitigate the outbreak. Repeated shutdown periods or permanently applied measures over the winter could be successful alternatives.

A new Lamarckian genetic algorithm for flexible ligand-receptor docking.

We present a Lamarckian genetic algorithm (LGA) variant for flexible ligand-receptor docking which allows to handle a large number of degrees of freedom. Our hybrid method combines a multi-deme LGA with a recently published gradient-based method for local optimization of molecular complexes. We compared the performance of our new hybrid method to two non gradient-based search heuristics on the Astex diverse set for flexible ligand-receptor docking. Our results show that the novel approach is clearly superior to other LGAs employing a stochastic optimization method. The new algorithm features a shorter run time and gives substantially better results, especially with increasing complexity of the ligands. Thus, it may be used to dock ligands with many rotatable bonds with high efficiency.

The significance of case detection ratios for predictions on the outcome of an epidemic - a message from mathematical modelers.

In attempting to predict the further course of the novel coronavirus disease (COVID-19) pandemic caused by SARS-CoV-2, mathematical models of different types are frequently employed and calibrated to reported case numbers. Among the major challenges in interpreting these data is the uncertainty about the amount of undetected infections, or conversely: the detection ratio. As a result, some models make assumptions about the percentage of detected cases among total infections while others completely neglect undetected cases. Here, we illustrate how model projections about case and fatality numbers vary significantly under varying assumptions on the detection ratio. Uncertainties in model predictions can be significantly reduced by representative testing, both for antibodies and active virus RNA, to uncover past and current infections that have gone undetected thus far.

Modeling the spread of COVID-19 in Germany: Early assessment and possible scenarios.

The novel coronavirus (SARS-CoV-2), identified in China at the end of December 2019 and causing the disease COVID-19, has meanwhile led to outbreaks all over the globe with about 2.2 million confirmed cases and more than 150,000 deaths as of April 17, 2020. In this work, mathematical models are used to reproduce data of the early evolution of the COVID-19 outbreak in Germany, taking into account the effect of actual and hypothetical non-pharmaceutical interventions. Systems of differential equations of SEIR type are extended to account for undetected infections, stages of infection, and age groups. The models are calibrated on data until April 5. Data from April 6 to 14 are used for model validation. We simulate different possible strategies for the mitigation of the current outbreak, slowing down the spread of the virus and thus reducing the peak in daily diagnosed cases, the demand for hospitalization or intensive care units admissions, and eventually the number of fatalities. Our results suggest that a partial (and gradual) lifting of introduced control measures could soon be possible if accompanied by further increased testing activity, strict isolation of detected cases, and reduced contact to risk groups.

A new method for the gradient-based optimization of molecular complexes.

We present a novel method for the local optimization of molecular complexes. This new approach is especially suited for usage in molecular docking. In molecular modeling, molecules are often described employing a compact representation to reduce the number of degrees of freedom. This compact representation is realized by fixing bond lengths and angles while permitting changes in translation, orientation, and selected dihedral angles. Gradient-based energy minimization of molecular complexes using this representation suffers from well-known singularities arising during the optimization process. We suggest an approach new in the field of structure optimization that allows to employ gradient-based optimization algorithms for such a compact representation. We propose to use exponential mapping to define the molecular orientation which facilitates calculating the orientational gradient. To avoid singularities of this parametrization, the local minimization algorithm is modified to change efficiently the orientational parameters while preserving the molecular orientation, i.e. we perform well-defined jumps on the objective function. Our approach is applicable to continuous, but not necessarily differentiable objective functions. We evaluated our new method by optimizing several ligands with an increasing number of internal degrees of freedom in the presence of large receptors. In comparison to the method of Solis and Wets in the challenging case of a non-differentiable scoring function, our proposed method leads to substantially improved results in all test cases, i.e. we obtain better scores in fewer steps for all complexes.

Mimotopes identify conformational B-cell epitopes on the two major house dust mite allergens Der p 1 and Der p 2.

House dust mite allergy occurs in 10-20% of the population. Improvement of the present immunotherapy requires detailed knowledge about the structure of the allergens. Mimotopes selected from phage peptide libraries imitate the conformational epitopes of a natural allergen. The aim of our study was to generate epitope mimics for the two major allergens of house dust mite. When the monoclonal anti-Der p 1 and anti-Der p 2 antibodies were used for biopannings, mimotopes were selected which bound also specific IgE from human allergic patients' sera. The conformational matching of these mimotopes on the 3D structure of the natural allergens determined discontinuous epitopes in both cases, representing conformational B-cell epitopes relevant for binding of human IgE. Therefore, these mimotopes are potential candidates for the directed induction of blocking antibodies and epitope-specific immunotherapy of mite allergy.

Anti-idiotypic Fab Fragments Image a Conserved N-terminal Epitope Patch of Grass Pollen Allergen Phl p 1.

BACKGROUND AND AIMS: Naturally occurring anti-idiotypic antibodies structurally mimic the original antibody epitope. Anti-idiotypes, therefore, are interesting tools for the portrayal of conformational B-cell epitopes of allergens. In this study we used this strategy particularly for major timothy grass pollen (Phleum pratense) allergen Phl p 1. METHODS AND RESULTS: We used a combinatorial phage display library constructed from the peripheral IgG repertoire of a grass pollen allergic patient which was supposed to contain anti-idiotypic Fab specificities. Using purified anti-Phl p 1 IgG for biopanning, several Fab displaying phage clones could be isolated. 100 amplified colonies were screened for their binding capacity to anti-Phl p 1-specific antibodies, finally resulting in four distinct Fab clones according to sequence analysis. Interestingly, heavy chains of all clones derived from the same germ line sequence and showed high homology in their CDRs. Projecting their sequence information on the surface of the natural allergen Phl p 1 (PDB ID: 1N10) indicated matches on the N-terminal domain of the homo-dimeric allergen, including the bridging region between the two monomers. The resulting epitope patches were formed by spatially distant sections of the primary allergen sequence. CONCLUSION: In this study we report that anti-idiotypic specificities towards anti-Phl p 1 IgG, selected from a Fab library of a grass pollen allergic patient, mimic a conformational epitope patch being distinct from a previously reported IgE epitope area.

BALLDock/SLICK: a new method for protein-carbohydrate docking.

Protein-ligand docking is an essential technique in computer-aided drug design. While generally available docking programs work well for most drug classes, carbohydrates and carbohydrate-like compounds are often problematic for docking. We present a new docking method specifically designed to handle docking of carbohydrate-like compounds. BALLDock/SLICK combines an evolutionary docking algorithm for flexible ligands and flexible receptor side chains with carbohydrate-specific scoring and energy functions. The scoring function has been designed to identify accurate ligand poses, while the energy function yields accurate estimates of the binding free energies of these poses. On a test set of known protein-sugar complexes we demonstrate the ability of the approach to generate correct poses for almost all of the structures and achieve very low mean errors for the predicted binding free energies.

Initiation of cytoskeletal asymmetry for cell polarization and movement.

A variety of mathematical models for the actin driven motility of eucaryotic cells have been discussed over the last decades. However, most of them do model polarized cells which are already in motion or at least have established lamellipods. Here we investigate the stimulus induced transition from a symmetric resting state of a cell to a polarized one. Our goal is to find a minimal scenario for this rearrangement of the cytoskeleton and to figure out which of the manifold proteins and processes associated with actin dynamics are essential for the initiation of movement.