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BackgroundCountries across Europe have faced similar evolutions of SARS-CoV-2 variants of concern, including the Alpha, Delta, and Omicron variants.Materials and methodsWe used data from GISAID and applied a robust, automated mathematical substitution model to study the dynamics of COVID-19 variants in Europe over a period of more than 2 years, from late 2020 to early 2023. This model identifies variant substitution patterns and distinguishes between residual and dominant behavior. We used weekly sequencing data from 19 European countries to estimate the increase in transmissibility (Δβ) between consecutive SARS-CoV-2 variants. In addition, we focused on large countries with separate regional outbreaks and complex scenarios of multiple competing variants.ResultsOur model accurately reproduced the observed substitution patterns between the Alpha, Delta, and Omicron major variants. We estimated the daily variant prevalence and calculated Δβ between variants, revealing that: (i) Δβ increased progressively from the Alpha to the Omicron variant; (ii) Δβ showed a high degree of variability within Omicron variants; (iii) a higher Δβ was associated with a later emergence of the variant within a country; (iv) a higher degree of immunization of the population against previous variants was associated with a higher Δβ for the Delta variant; (v) larger countries exhibited smaller Δβ, suggesting regionally diverse outbreaks within the same country; and finally (vi) the model reliably captures the dynamics of competing variants, even in complex scenarios.ConclusionThe use of mathematical models allows for precise and reliable estimation of daily cases of each variant. By quantifying Δβ, we have tracked the spread of the different variants across Europe, highlighting a robust increase in transmissibility trend from Alpha to Omicron. Additionally, we have shown that the geographical characteristics of a country, as well as the timing of new variant entrances, can explain some of the observed differences in variant substitution dynamics across countries.

IntroductionWe use Spanish data from August 2020 to March 2021 as a natural experiment to analyze how a standardized measure of COVID-19 growth correlates with asymmetric meteorological and mobility situations in 48 Spanish provinces. The period of time is selected prior to vaccination so that the level of susceptibility was high, and during geographically asymmetric implementation of non-pharmacological interventions.MethodsWe develop reliable aggregated mobility data from different public sources and also compute the average meteorological time series of temperature, dew point, and UV radiance in each Spanish province from satellite data. We perform a dimensionality reduction of the data using principal component analysis and investigate univariate and multivariate correlations of mobility and meteorological data with COVID-19 growth.ResultsWe find significant, but generally weak, univariate correlations for weekday aggregated mobility in some, but not all, provinces. On the other hand, principal component analysis shows that the different mobility time series can be properly reduced to three time series. A multivariate time-lagged canonical correlation analysis of the COVID-19 growth rate with these three time series reveals a highly significant correlation, with a median R-squared of 0.65. The univariate correlation between meteorological data and COVID-19 growth is generally not significant, but adding its two main principal components to the mobility multivariate analysis increases correlations significantly, reaching correlation coefficients between 0.6 and 0.98 in all provinces with a median R-squared of 0.85. This result is robust to different approaches in the reduction of dimensionality of the data series.DiscussionOur results suggest an important effect of mobility on COVID-19 cases growth rate. This effect is generally not observed for meteorological variables, although in some Spanish provinces it can become relevant. The correlation between mobility and growth rate is maximal at a time delay of 2-3 weeks, which agrees well with the expected 5?10 day delays between infection, development of symptoms, and the detection/report of the case.

PurposeWe aim to compare the severity of infections between omicron and delta variants in 609,352 SARS-CoV-2 positive cases using local hospitalization, vaccination, and variants data from the Catalan Health Care System (which covers around 7. 8 million people).MethodsWe performed a substitution model to establish the increase in transmissibility of omicron using variant screening data from primary care practices (PCP) and hospital admissions. In addition, we used this data from PCP to establish the two periods when delta and omicron were, respectively, dominant (above 95% of cases). After that, we performed a population-based cohort analysis to calculate the rates of hospital and intensive care unit (ICU) admissions for both periods and to estimate reduction in severity. Rate ratios (RR) and 95% confidence intervals (95% CI) were calculated and stratified by age and vaccination status. In a second analysis, the differential substitution model in primary care vs. hospitals allowed us to obtain a population-level average change in severity.ResultsWe have included 48,874 cases during the delta period and 560,658 during the omicron period. During the delta period, on average, 3.8% of the detected cases required hospitalization for COVID-19. This percentage dropped to 0.9% with omicron [RR of 0.46 (95% CI: 0.43 to 0.49)]. For ICU admissions, it dropped from 0.8 to 0.1% [RR 0.25 (95% CI: 0.21 to 0.28)]. The proportion of cases hospitalized or admitted to ICU was lower in the vaccinated groups, independently of the variant. Omicron was associated with a reduction in risk of admission to hospital and ICU in all age and vaccination status strata. The differential substitution models showed an average RR between 0.19 and 0.50.ConclusionBoth independent methods consistently show an important decrease in severity for omicron relative to delta. The systematic reduction happens regardless of age. The severity is also reduced for non-vaccinated and vaccinated groups, but it remains always higher in the non-vaccinated population. This suggests an overall reduction in severity, which could be intrinsic to the omicron variant. The fact is that the RR in ICU admission is systematically smaller than in hospitalization points in the same direction.

Regulation of intracellular calcium is a critical component of cardiac electrophysiology and excitation-contraction coupling. The calcium spark, the fundamental element of the intracellular calcium transient, is initiated in specialized nanodomains which co-locate the ryanodine receptors and L-type calcium channels. However, calcium homeostasis is ultimately regulated at the cellular scale, by the interaction of spatially separated but diffusively coupled nanodomains with other sub-cellular and surface-membrane calcium transport channels with strong non-linear interactions; and cardiac electrophysiology and arrhythmia mechanisms are ultimately tissue-scale phenomena, regulated by the interaction of a heterogeneous population of coupled myocytes. Recent advances in imaging modalities and image-analysis are enabling the super-resolution reconstruction of the structures responsible for regulating calcium homeostasis, including the internal structure of nanodomains themselves. Extrapolating functional and imaging data from the nanodomain to the whole-heart is non-trivial, yet essential for translational insight into disease mechanisms. Computational modeling has important roles to play in relating structural and functional data at the sub-cellular scale and translating data across the scales. This review covers recent methodological advances that enable image-based modeling of the single nanodomain and whole cardiomyocyte, as well as the development of multi-scale simulation approaches to integrate data from nanometer to whole-heart. Firstly, methods to overcome the computational challenges of simulating spatial calcium dynamics in the nanodomain are discussed, including image-based modeling at this scale. Then, recent whole-cell models, capable of capturing a range of different structures (such as the T-system and mitochondria) and cellular heterogeneity/variability are discussed at two different levels of discretization. Novel methods to integrate the models and data across the scales and simulate stochastic dynamics in tissue-scale models are then discussed, enabling elucidation of the mechanisms by which nanodomain remodeling underlies arrhythmia and contractile dysfunction. Perspectives on model differences and future directions are provided throughout.

The development of modeling structures at the channel level that can integrate subcellular and cell models and properly reproduce different experimental data is of utmost importance in cardiac electrophysiology. In contrast to gate-based models, Markov Chain models are well suited to promote the integration of the subcellular level of the cardiomyocyte to the whole cell. In this paper, we develop Markov Chain models for the L-type Calcium current that can reproduce the electrophysiology of two established human models for the ventricular and Purkinje cells. In addition, instead of presenting a single set of parameters, we present a collection of set of parameters employing Differential Evolution algorithms that can properly reproduce very different protocol data. We show the importance of using an ensemble of a set of parameter values to obtain proper results when considering a second protocol that suppresses calcium inactivation and mimics a pathological condition. We discuss how model discrepancy, data availability, and parameter identifiability can influence the choice of the size of the collection. In summary, we have modified two cardiac models by proposing new Markov Chain models for the L-type Calcium. We keep the original whole-cell dynamics by reproducing the same characteristic action potential and calcium dynamics, whereas the Markov chain-based description of the L-type Calcium channels allows novel small spatial scale simulations of subcellular processes. Finally, the use of collections of parameters was crucial for addressing model discrepancy, identifiability issues, and avoiding fitting parameters overly precisely, i.e., overfitting.

The current worldwide pandemic produced by coronavirus disease 2019 (COVID-19) has changed the paradigm of mathematical epidemiology due to the high number of unknowns of this new disease. Thus, the empirical approach has emerged as a robust tool to analyze the actual situation carried by the countries and also allows us to predict the incoming scenarios. In this paper, we propose three empirical indexes to estimate the state of the pandemic. These indexes quantify both the propagation and the number of estimated cases, allowing us to accurately determine the real risk of a country. We have calculated these indexes' evolution for several European countries. Risk diagrams are introduced as a tool to visualize the evolution of a country and evaluate its current risk as a function of the number of contagious individuals and the empiric reproduction number. Risk diagrams at the regional level are useful to observe heterogeneity on COVID-19 penetration and spreading in some countries, which is essential during deconfinement processes. During the pandemic, there have been significant differences seen in countries reporting case criterion and detection capacity. Therefore, we have introduced estimations about the real number of infectious cases that allows us to have a broader view and to better estimate the risk. These diagrams and indexes have been successfully used for the monitoring of European countries and regions during the COVID-19 pandemic.

Policymakers need clear, fast assessment of the real spread of the COVID-19 epidemic in each of their respective countries. Standard measures of the situation provided by the governments include reported positive cases and total deaths. While total deaths indicate immediately that countries like Italy and Spain had the worst situation as of mid-April, 2020, reported cases alone do not provide a complete picture of the situation. Different countries diagnose differently and present very distinctive reported case fatality ratios. Similar levels of reported incidence and mortality might hide a very different underlying pictures. Here we present a straightforward and robust estimation of the diagnostic rate in each European country. From that estimation we obtain a uniform, unbiased incidence of the epidemic. The method to obtain the diagnostic rate is transparent and empirical. The key assumption of the method is that the infection fatality ratio of COVID-19 in Europe is not strongly country-dependent. We show that this number is not expected to be biased due to demography nor to the way total deaths are reported. The estimation protocol is dynamic, and it has been yielding converging numbers for diagnostic rates in all European countries as from mid-April, 2020. Using this diagnostic rate, policy makers can obtain Effective Potential Growth updated every day, providing an unbiased assessment of the countries at greater risk of experiencing an uncontrolled situation. The method developed has been and will be used to track possible improvements in the diagnostic rate in European countries as the epidemic evolves.

The appearance and fast spreading of Covid-19 took the international community by surprise. Collaboration between researchers, public health workers, and politicians has been established to deal with the epidemic. One important contribution from researchers in epidemiology is the analysis of trends so that both the current state and short-term future trends can be carefully evaluated. Gompertz model has been shown to correctly describe the dynamics of cumulative confirmed cases, since it is characterized by a decrease in growth rate showing the effect of control measures. Thus, it provides a way to systematically quantify the Covid-19 spreading velocity and it allows short-term predictions and longer-term estimations. This model has been employed to fit the cumulative cases of Covid-19 from several European countries. Results show that there are systematic differences in spreading velocity among countries. The model predictions provide a reliable picture of the short-term evolution in countries that are in the initial stages of the Covid-19 outbreak, and may permit researchers to uncover some characteristics of the long-term evolution. These predictions can also be generalized to calculate short-term hospital and intensive care units (ICU) requirements.

Calcium oscillations and waves induce depolarization in cardiac cells which are believed to cause life-threathening arrhythimas. In this work, we study the conditions for the appearance of calcium oscillations in both a detailed subcellular model of calcium dynamics and a minimal model that takes into account just the minimal ingredients of the calcium toolkit. To avoid the effects of homeostatic changes and the interaction with the action potential we consider the somewhat artificial condition of a cell without pacing and with no calcium exchange with the extracellular medium. Both the full subcellular model and the minimal model present the same scenarios depending on the calcium load: two stationary states, one with closed ryanodine receptors (RyR) and most calcium in the cell stored in the sarcoplasmic reticulum (SR), and another, with open RyRs and a depleted SR. In between, calcium oscillations may appear. The robustness of these oscillations is determined by the amount of calsequestrin (CSQ). The lack of this buffer in the SR enhances the appearance of oscillations. The minimal model allows us to relate the stability of the oscillating state to the nullcline structure of the system, and find that its range of existence is bounded by a homoclinic and a Hopf bifurcation, resulting in a sudden transition to the oscillatory regime as the cell calcium load is increased. Adding a small amount of noise to the RyR behavior increases the parameter region where oscillations appear and provides a gradual transition from the resting state to the oscillatory regime, as observed in the subcellular model and experimentally.

Ventricular contraction is roughly proportional to the amount of calcium released from the Sarcoplasmic Reticulum (SR) during systole. While it is rather straightforward to measure calcium levels and contractibility under different physiological conditions, the complexity of calcium handling during systole and diastole has made the prediction of its release at steady state impossible. Here we approach the problem analyzing the evolution of intracellular and extracellular calcium fluxes during a single beat which is away from homeostatic balance. Using an in-silico subcellular model of rabbit ventricular myocyte, we show that the high dimensional nonlinear problem of finding the steady state can be reduced to a two-variable general equilibrium condition where pre-systolic calcium level in the cytosol and in the SR must fulfill simultaneously two different equalities. This renders calcium homeostasis as a problem that can be studied in terms of its equilibrium structure, leading to precise predictions of steady state from single-beat measurements. We show how changes in ion channels modify the general equilibrium, as shocks would do in general equilibrium macroeconomic models. This allows us to predict when an enhanced entrance of calcium in the cell reduces its contractibility and explain why SERCA gene therapy, a change in calcium handling to treat heart failure, might fail to improve contraction even when it successfully increases SERCA expression.

The COVID-19 pandemic is changing the world in unprecedented and unpredictable ways. Human mobility, being the greatest facilitator for the spread of the virus, is at the epicenter of this change. In order to study mobility under COVID-19, to evaluate the efficiency of mobility restriction policies, and to facilitate a better response to future crisis, we need to understand all possible mobility data sources at our disposal. Our work studies private mobility sources, gathered from mobile-phones and released by large technological companies. These data are of special interest because, unlike most public sources, it is focused on individuals rather than on transportation means. Furthermore, the sample of society they cover is large and representative. On the other hand, these data are not directly accessible for anonymity reasons. Thus, properly interpreting its patterns demands caution. Aware of that, we explore the behavior and inter-relations of private sources of mobility data in the context of Spain. This country represents a good experimental setting due to both its large and fast pandemic peak and its implementation of a sustained, generalized lockdown. Our work illustrates how a direct and naive comparison between sources can be misleading, as certain days (e.g., Sundays) exhibit a directly adverse behavior. After understanding their particularities, we find them to be partially correlated and, what is more important, complementary under a proper interpretation. Finally, we confirm that mobile-data can be used to evaluate the efficiency of implemented policies, detect changes in mobility trends, and provide insights into what new normality means in Spain.

IntroductionBronchiolitis, mostly caused by Respiratory Syncytial Virus (RSV), and influenza among other respiratory infections, lead to seasonal saturation at healthcare centers in temperate areas. There is no gold standard to characterize the stages of epidemics, nor the risk of respiratory infections growing. We aimed to define a set of indicators to assess the risk level of respiratory viral epidemics, based on both incidence and their short-term dynamics, and considering epidemical thresholds.MethodsWe used publicly available data on daily cases of influenza for the whole population and bronchiolitis in children

Monitoring transmission is a prerequisite for containing COVID-19. We report on effective potential growth (EPG) as a novel measure for the early identification of local outbreaks based on primary care electronic medical records (EMR) and PCR-confirmed cases. Secondly, we studied whether increasing EPG precedes local hospital and intensive care (ICU) admissions and mortality. Population-based cohort including all Catalan citizens' PCR tests, hospitalization, intensive care (ICU) and mortality between 1/07/2020 and 13/09/2020; linked EMR covering 88.6% of the Catalan population was obtained. Nursing home residents were excluded. COVID-19 counts were ascertained based on EMR and PCRs separately. Weekly empirical propagation (ρ7) and 14-day cumulative incidence (A14) and 95% confidence intervals were estimated at care management area (CMA) level, and combined as EPG = ρ7 × A14. Overall, 7,607,201 and 6,798,994 people in 43 CMAs were included for PCR and EMR measures, respectively. A14, ρ7, and EPG increased in numerous CMAs during summer 2020. EMR identified 2.70-fold more cases than PCRs, with similar trends, a median (interquartile range) 2 (1) days earlier, and better precision. Upticks in EPG preceded increases in local hospital admissions, ICU occupancy, and mortality. Increasing EPG identified localized outbreaks in Catalonia, and preceded local hospital and ICU admissions and subsequent mortality. EMRs provided similar estimates to PCR, but some days earlier and with better precision. EPG is a useful tool for the monitoring of community transmission and for the early identification of COVID-19 local outbreaks.