Background The COVID-19 pandemic has led to a high interest in mathematical models describing and predicting the diverse aspects and implications of the virus outbreak. Model results represent an important part of the information base for the decision process on different administrative levels. The Robert-Koch-Institute (RKI) initiated a project whose main goal is to predict COVID-19-specific occupation of beds in intensive care units: Steuerungs-Prognose von Intensivmedizinischen COVID-19 Kapazitäten (SPoCK). The incidence of COVID-19 cases is a crucial predictor for this occupation. Methods We developed a model based on ordinary differential equations for the COVID-19 spread with a time-dependent infection rate described by a spline. Furthermore, the model explicitly accounts for weekday-specific reporting and adjusts for reporting delay. The model is calibrated in a purely data-driven manner by a maximum likelihood approach. Uncertainties are evaluated using the profile likelihood method. The uncertainty about the appropriate modeling assumptions can be accounted for by including and merging results of different modelling approaches. The analysis uses data from Germany describing the COVID-19 spread from early 2020 until March 31st, 2021. Results The model is calibrated based on incident cases on a daily basis and provides daily predictions of incident COVID-19 cases for the upcoming three weeks including uncertainty estimates for Germany and its subregions. Derived quantities such as cumulative counts and 7-day incidences with corresponding uncertainties can be computed. The estimation of the time-dependent infection rate leads to an estimated reproduction factor that is oscillating around one. Data-driven estimation of the dark figure purely from incident cases is not feasible. Conclusions We successfully implemented a procedure to forecast near future COVID-19 incidences for diverse subregions in Germany which are made available to various decision makers via an interactive web application. Results of the incidence modeling are also used as a predictor for forecasting the need of intensive care units.
BackgroundThe COVID-19 pandemic has led to a high interest in mathematical models describing and predicting the diverse aspects and implications of the virus outbreak. Model results represent an important part of the information base for the decision process on different administrative levels. The Robert-Koch-Institute (RKI) initiated a project whose main goal is to predict COVID-19-specific occupation of beds in intensive care units: Steuerungs-Prognose von Intensivmedizinischen COVID-19 Kapazitäten (SPoCK). The incidence of COVID-19 cases is a crucial predictor for this occupation.MethodsWe developed a model based on ordinary differential equations for the COVID-19 spread with a time-dependent infection rate described by a spline. Furthermore, the model explicitly accounts for weekday-specific reporting and adjusts for reporting delay. The model is calibrated in a purely data-driven manner by a maximum likelihood approach. Uncertainties are evaluated using the profile likelihood method. The uncertainty about the appropriate modeling assumptions can be accounted for by including and merging results of different modelling approaches.ResultsThe model is calibrated based on incident cases on a daily basis and provides daily predictions of incident COVID-19 cases for the upcoming three weeks including uncertainty estimates for Germany and its subregions. Derived quantities such as cumulative counts and 7-day incidences with corresponding uncertainties can be computed. The estimation of the time-dependent infection rate leads to an estimated reproduction factor that is oscillating around one. Data-driven estimation of the dark figure purely from incident cases is not feasible.ConclusionsWe successfully implemented a procedure to forecast near future COVID-19 incidences for diverse subregions in Germany which are made available to various decision makers via an interactive web application. Results of the incidence modeling are also used as a predictor for forecasting the need of intensive care units.
Tissue functions are determined by the types and ratios of cells present, but little is known about self-organizing principles establishing correct cell type compositions. Mucociliary airway clearance relies on the correct balance between secretory and ciliated cells, which is regulated by Notch signaling across mucociliary systems. Using the airway-like Xenopus epidermis, we investigate how cell fates depend on signaling, how signaling levels are controlled, and how Hes transcription factors regulate cell fates. We show that four mucociliary cell types each require different Notch levels and that their specification is initiated sequentially by a temporal Notch gradient. We describe a novel role for Foxi1 in the generation of Delta-expressing multipotent progenitors through Hes7.1. Hes7.1 is a weak repressor of mucociliary genes and overcomes maternal repression by the strong repressor Hes2 to initiate mucociliary development. Increasing Notch signaling then inhibits Hes7.1 and activates first Hes4, then Hes5.10, which selectively repress cell fates. We have uncovered a self-organizing mechanism of mucociliary cell type composition by competitive de-repression of cell fates by a set of differentially acting repressors. Furthermore, we present an in silico model of this process with predictive abilities.
Zusammenfassung Hintergrund Zeitdynamische Prognosemodelle spielen eine zentrale Rolle zur Steuerung von intensivmedizinischen COVID-19-Kapazitäten im Pandemiegeschehen. Ein wichtiger Vorhersagewert (Prädiktor) für die zukünftige intensivmedizinische (ITS-)COVID-19-Bettenbelegungen ist die Anzahl der SARS-CoV-2-Neuinfektionen in der Bevölkerung, die wiederum stark von Schwankungen im Wochenverlauf, Meldeverzug, regionalen Unterschieden, Dunkelziffer, zeitabhängiger Ansteckungsrate, Impfungen, SARS-CoV-2-Virusvarianten sowie von nichtpharmazeutischen Eindämmungsmaßnahmen abhängt. Darüber hinaus wird die aktuelle und auch zukünftige COVID-ITS-Belegung maßgeblich von den intensivmedizinischen Entlassungs- und Sterberaten beeinflusst. Methode Sowohl die Anzahl der SARS-CoV-2-Neuinfektionen in der Bevölkerung als auch die intensivmedizinischen COVID-19-Bettenbelegungen werden bundesweit flächendeckend erfasst. Diese Daten werden tagesaktuell mit epidemischen SEIR-Modellen aus gewöhnlichen Differenzialgleichungen und multiplen Regressionsmodellen statistisch analysiert. Ergebnisse Die Prognoseergebnisse der unmittelbaren Entwicklung (20-Tage-Vorhersage) der ITS-Belegung durch COVID-19-Patienten*innen werden Entscheidungsträgern auf verschiedenen überregionalen Ebenen zur Verfügung gestellt. Schlussfolgerung Die Prognosen werden der Entwicklung von betreibbaren intensivmedizinischen Bettenkapazitäten gegenübergestellt, um frühzeitig Kapazitätsengpässe zu erkennen und kurzfristig reaktive Handlungssteuerungen, wie etwa überregionale Verlegungen, zu ermöglichen.
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