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

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.

Data suggested hospitalization as critical indicator of the severity of the COVID-19 pandemic, even at its early stages

COVID-19 has been spreading widely since January 2020, prompting the implementation of non-pharmaceutical interventions and vaccinations to prevent overwhelming the healthcare system. Our study models four waves of the epidemic in Munich over two years using a deterministic, biology-based mathematical model of SEIR type that incorporates both non-pharmaceutical interventions and vaccinations. We analyzed incidence and hospitalization data from Munich hospitals and used a two-step approach to fit the model parameters: first, we modeled incidence without hospitalization, and then we extended the model to include hospitalization compartments using the previous estimates as a starting point. For the first two waves, changes in key parameters, such as contact reduction and increasing vaccinations, were enough to represent the data. For wave three, the introduction of vaccination compartments was essential. In wave four, reducing contacts and increasing vaccinations were critical parameters for controlling infections. The importance of hospitalization data was highlighted, as it should have been included as a crucial parameter from the outset, along with incidence, to avoid miscommunication with the public. The emergence of milder variants like Omicron and a significant proportion of vaccinated people has made this fact even more evident.

Integrative modelling of reported case numbers and seroprevalence reveals time-dependent test efficiency and infectious contacts

Mathematical models have been widely used during the ongoing SARS-CoV-2 pandemic for data interpretation, forecasting, and policy making. However, most models are based on officially reported case numbers, which depend on test availability and test strategies. The time dependence of these factors renders interpretation difficult and might even result in estimation biases. Here, we present a computational modelling framework that allows for the integration of reported case numbers with seroprevalence estimates obtained from representative population cohorts. To account for the time dependence of infection and testing rates, we embed flexible splines in an epidemiological model. The parameters of these splines are estimated, along with the other parameters, from the available data using a Bayesian approach. The application of this approach to the official case numbers reported for Munich (Germany) and the seroprevalence reported by the prospective COVID-19 Cohort Munich (KoCo19) provides first estimates for the time dependence of the under-reporting factor. Furthermore, we estimate how the effectiveness of non-pharmaceutical interventions and of the testing strategy evolves over time. Overall, our results show that the integration of temporally highly resolved and representative data is beneficial for accurate epidemiological analyses.

Nutritional changes during the COVID-19 pandemic: a rapid scoping review on the impact of psychological factors

COVID-19 and the resulting measures to curb the spread of the virus have significantly changed our lives, including our nutritional choices. In this rapid scoping review an overview is provided of what psychological factors may be associated with peoples' eating behaviour during COVID-19 restrictions. Relevant literature was identified using PubMed, PsycInfo, CINAHL and MEDLINE databases from 2019 onwards. For included studies, information on study characteristics, eating behaviours, and psychological factors were extracted. 118 articles were included, representing 30 countries. Findings indicated that most people consumed more and unhealthy food in times of COVID-19 restrictions, while some consumed less but often for the wrong reasons. Several psychological factors, related to (1) affective reactions, (2) anxiety, fear and worriers, (3) stress and (4) subjective and mental wellbeing were found to be associated with this increase in food consumption. These outcomes may help to be better inform future interventions, and with that, to be better prepared in case of future lockdown scenarios.

Intensity and lag-time of non-pharmaceutical interventions on COVID-19 dynamics in German hospitals

Introduction

Evaluating the potential effects of non-pharmaceutical interventions on COVID-19 dynamics is challenging and controversially discussed in the literature. The reasons are manifold, and some of them are as follows. First, interventions are strongly correlated, making a specific contribution difficult to disentangle; second, time trends (including SARS-CoV-2 variants, vaccination coverage and seasonality) influence the potential effects; third, interventions influence the different populations and dynamics with a time delay.

Methods

In this article, we apply a distributed lag linear model on COVID-19 data from Germany from January 2020 to June 2022 to study intensity and lag time effects on the number of hospital patients and the number of prevalent intensive care patients diagnosed with polymerase chain reaction tests. We further discuss how the findings depend on the complexity of accounting for the seasonal trends.

Results and discussion

Our findings show that the first reducing effect of non-pharmaceutical interventions on the number of prevalent intensive care patients before vaccination can be expected not before a time lag of 5 days; the main effect is after a time lag of 10-15 days. In general, we denote that the number of hospital and prevalent intensive care patients decrease with an increase in the overall non-pharmaceutical interventions intensity with a time lag of 9 and 10 days. Finally, we emphasize a clear interpretation of the findings noting that a causal conclusion is challenging due to the lack of a suitable experimental study design.

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.

Bracher et al. compare 15 forecasting models of COVID-19 cases and deaths in Germany and Poland between January and mid-April 2021. Many, though not all, models outperform a simple baseline model up to four weeks ahead, with ensemble methods showing very good relative performance.

Using simulation modelling and systems science to help contain COVID-19: A systematic review

This study systematically reviews applications of three simulation approaches, that is, system dynamics model (SDM), agent-based model (ABM) and discrete event simulation (DES), and their hybrids in COVID-19 research and identifies theoretical and application innovations in public health. Among the 372 eligible papers, 72 focused on COVID-19 transmission dynamics, 204 evaluated both pharmaceutical and non-pharmaceutical interventions, 29 focused on the prediction of the pandemic and 67 investigated the impacts of COVID-19. ABM was used in 275 papers, followed by 54 SDM papers, 32 DES papers and 11 hybrid model papers. Evaluation and design of intervention scenarios are the most widely addressed area accounting for 55% of the four main categories, that is, the transmission of COVID-19, prediction of the pandemic, evaluation and design of intervention scenarios and societal impact assessment. The complexities in impact evaluation and intervention design demand hybrid simulation models that can simultaneously capture micro and macro aspects of the socio-economic systems involved.

Optimal control strategies for the reliable and competitive mathematical analysis of Covid-19 pandemic model

To understand dynamics of the COVID-19 disease realistically, a new SEIAPHR model has been proposed in this article where the infectious individuals have been categorized as symptomatic, asymptomatic, and super-spreaders. The model has been investigated for existence of a unique solution. To measure the contagiousness of COVID-19, reproduction numberR 0 is also computed using next generation matrix method. It is shown that the model is locally stable at disease-free equilibrium point whenR 0 < 1 and unstable forR 0 > 1 . The model has been analyzed for global stability at both of the disease-free and endemic equilibrium points. Sensitivity analysis is also included to examine the effect of parameters of the model on reproduction numberR 0 . A couple of optimal control problems have been designed to study the effect of control strategies for disease control and eradication from the society. Numerical results show that the adopted control approaches are much effective in reducing new infections.

A data-validated temporary immunity model of COVID-19 spread in Michigan

We introduce a distributed-delay differential equation disease spread model for COVID-19 spread. The model explicitly incorporates the population's time-dependent vaccine uptake and incorporates a gamma-distributed temporary immunity period for both vaccination and previous infection. We validate the model on COVID-19 cases and deaths data from the state of Michigan and use the calibrated model to forecast the spread and impact of the disease under a variety of realistic booster vaccine strategies. The model suggests that the mean immunity duration for individuals after vaccination is 350 days and after a prior infection is 242 days. Simulations suggest that both high population-wide adherence to vaccination mandates and a more-than-annually frequency of booster doses will be required to contain outbreaks in the future.

On the Parametrization of Epidemiologic Models—Lessons from Modelling COVID-19 Epidemic

Numerous prediction models of SARS-CoV-2 pandemic were proposed in the past. Unknown parameters of these models are often estimated based on observational data. However, lag in case-reporting, changing testing policy or incompleteness of data lead to biased estimates. Moreover, parametrization is time-dependent due to changing age-structures, emerging virus variants, non-pharmaceutical interventions, and vaccination programs. To cover these aspects, we propose a principled approach to parametrize a SIR-type epidemiologic model by embedding it as a hidden layer into an input-output non-linear dynamical system (IO-NLDS). Observable data are coupled to hidden states of the model by appropriate data models considering possible biases of the data. This includes data issues such as known delays or biases in reporting. We estimate model parameters including their time-dependence by a Bayesian knowledge synthesis process considering parameter ranges derived from external studies as prior information. We applied this approach on a specific SIR-type model and data of Germany and Saxony demonstrating good prediction performances. Our approach can estimate and compare the relative effectiveness of non-pharmaceutical interventions and provide scenarios of the future course of the epidemic under specified conditions. It can be translated to other data sets, i.e., other countries and other SIR-type models.

Regional opening strategies with commuter testing and containment of new SARS-CoV-2 variants in Germany

BACKGROUND

Despite the vaccination process in Germany, a large share of the population is still susceptible to SARS-CoV-2. In addition, we face the spread of novel variants. Until we overcome the pandemic, reasonable mitigation and opening strategies are crucial to balance public health and economic interests.

METHODS

We model the spread of SARS-CoV-2 over the German counties by a graph-SIR-type, metapopulation model with particular focus on commuter testing. We account for political interventions by varying contact reduction values in private and public locations such as homes, schools, workplaces, and other. We consider different levels of lockdown strictness, commuter testing strategies, or the delay of intervention implementation. We conduct numerical simulations to assess the effectiveness of the different intervention strategies after one month. The virus dynamics in the regions (German counties) are initialized randomly with incidences between 75 and 150 weekly new cases per 100,000 inhabitants (red zones) or below (green zones) and consider 25 different initial scenarios of randomly distributed red zones (between 2 and 20% of all counties). To account for uncertainty, we consider an ensemble set of 500 Monte Carlo runs for each scenario.

RESULTS

We find that the strength of the lockdown in regions with out of control virus dynamics is most important to avoid the spread into neighboring regions. With very strict lockdowns in red zones, commuter testing rates of twice a week can substantially contribute to the safety of adjacent regions. In contrast, the negative effect of less strict interventions can be overcome by high commuter testing rates. A further key contributor is the potential delay of the intervention implementation. In order to keep the spread of the virus under control, strict regional lockdowns with minimum delay and commuter testing of at least twice a week are advisable. If less strict interventions are in favor, substantially increased testing rates are needed to avoid overall higher infection dynamics.

CONCLUSIONS

Our results indicate that local containment of outbreaks and maintenance of low overall incidence is possible even in densely populated and highly connected regions such as Germany or Western Europe. While we demonstrate this on data from Germany, similar patterns of mobility likely exist in many countries and our results are, hence, generalizable to a certain extent.

Association of anti-contagion policies with the spread of COVID-19 in United States

BACKGROUND

The outbreak of a novel coronavirus, known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), or COVID-19, raised worldwide concern. The present study investigates the association between anti-contagion policies and the spread of COVID-19 across the United States.

DESIGN AND METHODS

We selected the most frequently implemented COVID-19 anti-contagion policies in all the U.S. states issued from 29 February 2020. Accordingly, we modified an epidemiological model and combined it with a comprehensive statistical analysis to evaluate the policies' individual and overall likely impact.

RESULTS

For the first time, a novel index, evaluates the associations between policy implementation and COVID-19 spread at both statewide and national levels. Our results indicate that governmental policies requiring mask use, businesses social distancing, and quarantining travelers may be most effective for controlling COVID-19 spread. Simultaneously, widespread orders like school closure and safer-at-home that can be particularly disruptive to the economy and social fabric of society may be unnecessary given their lack of association with reducing infection.

CONCLUSIONS

The absence of any COVID-19 vaccines during the first several months of its pandemic necessitated using governmental policies to help stop the spread of this disease. Our index showed the association between implemented policies and COVID-19 spread, highlighting the specific policies with the greatest association - mandatory quarantine upon entering a state, businesses implementing social distancing, and mandatory mask use - and those with less association like school closure and safer-at-home orders. This study provided evidence to inform policy choices for the current global crisis and future pandemics.

Mathematical modeling of COVID-19 pandemic in the context of sub-Saharan Africa: a short-term forecasting in Cameroon and Gabon

In this paper, we propose and analyse a compartmental model of COVID-19 to predict and control the outbreak. We first formulate a comprehensive mathematical model for the dynamical transmission of COVID-19 in the context of sub-Saharan Africa. We provide the basic properties of the model and compute the basic reproduction number $\mathcal {R}_0$ when the parameter values are constant. After, assuming continuous measurement of the weekly number of newly COVID-19 detected cases, newly deceased individuals and newly recovered individuals, the Ensemble of Kalman filter (EnKf) approach is used to estimate the unmeasured variables and unknown parameters, which are assumed to be time-dependent using real data of COVID-19. We calibrated the proposed model to fit the weekly data in Cameroon and Gabon before, during and after the lockdown. We present the forecasts of the current pandemic in these countries using the estimated parameter values and the estimated variables as initial conditions. During the estimation period, our findings suggest that $\mathcal {R}_0 \approx 1.8377 $ in Cameroon, while $\mathcal {R}_0 \approx 1.0379$ in Gabon meaning that the disease will not die out without any control measures in theses countries. Also, the number of undetected cases remains high in both countries, which could be the source of the new wave of COVID-19 pandemic. Short-term predictions firstly show that one can use the EnKf to predict the COVID-19 in Sub-Saharan Africa and that the second vague of the COVID-19 pandemic will still increase in the future in Gabon and in Cameroon. A comparison between the basic reproduction number from human individuals $\mathcal {R}_{0h}$ and from the SARS-CoV-2 in the environment $\mathcal {R}_{0v}$ has been done in Cameroon and Gabon. A comparative study during the estimation period shows that the transmissions from the free SARS-CoV-2 in the environment is greater than that from the infected individuals in Cameroon with $\mathcal {R}_{0h}$ = 0.05721 and $\mathcal {R}_{0v}$ = 1.78051. This imply that Cameroonian apply distancing measures between individual more than with the free SARS-CoV-2 in the environment. But, the opposite is observed in Gabon with $\mathcal {R}_{0h}$ = 0.63899 and $\mathcal {R}_{0v}$ = 0.39894. So, it is important to increase the awareness campaigns to reduce contacts from individual to individual in Gabon. However, long-term predictions reveal that the COVID-19 detected cases will play an important role in the spread of the disease. Further, we found that there is a necessity to increase timely the surveillance by using an awareness program and a detection process, and the eradication of the pandemic is highly dependent on the control measures taken by each government.

A Mathematical Study of COVID-19 Spread by Vaccination Status in Virginia

We introduce a novel n-stage vaccination model and corresponding system of differential equations that stratify a population according to their vaccination status. The model is an extension of the classical SIR-type models commonly used for time-course simulations of infectious disease spread and allows for the mitigation effects of vaccination to be uncoupled from other factors, such as changes in social behavior and the prevalence of virus variants. We fit the model to the Virginia Department of Health data on new COVID-19 cases, hospitalizations, and deaths broken down by vaccination status. The model suggests that, from 23 January through 11 September, fully vaccinated individuals were 89.8% less likely to become infected with COVID-19 and that the B.1.617.2 (Delta) variant is 2.08 times more transmissible than previously circulating strains of COVID-19. We project the model trajectories into the future to predict the impact of booster shots.

Are the upper bounds for new SARS-CoV-2 infections in Germany useful?

At the end of 2019, an outbreak of a new coronavirus, called SARS–CoV–2, was reported in China and later in other parts of the world. First infection reported in Germany by the end of January 2020 and on March 16th, 2020 the federal government announced a partial lockdown in order to mitigate the spread. Since the dynamics of new infections started to slow down, German states started to relax the confinement measures as to May 6th, 2020. As a fall back option, a limit of 50 new infections per 100,000 inhabitants within seven days was introduced for each district in Germany. If a district exceeds this limit, measures to control the spread of the virus should be taken. Based on a multi–patch SEAIRD–type model, we will simulate the effect of choosing a specific upper limit for new infections. We investigate, whether the politically motivated bound is low enough to detect new outbreaks at an early stage. Subsequently, we introduce an optimal control problem to tackle the multi–criteria problem of finding a bound for new infections that is low enough to avoid new outbreaks, which might lead to an overload of the health care system, but is large enough to curb the expected economic losses.

Resuming Dental and Craniomaxillofacial Surgical Missions During the COVID-19 Pandemic: Guidelines and Recommendations

Study Design

Descriptive review article.

Objective

The purpose of this article is to provide guidelines and recommendations for how to safely resume dental and craniomaxillofacial STSMs. The following considerations will be discussed: the need for extensive collaboration between organizations and local leadership, the importance of COVID-19 testing, use and management of personal protective equipment, team selection and training, social distancing protocols, and criteria for patient and case selection.

Methods

A literature review was completed, identifying resources and current data regarding the safe resumption clinical activities during the COVID-19 pandemic.

Results

At this time, there are no protocols developed regarding the safe resumption of STSMs. Primary resources, including the CDC, WHO, and FDA should be closely monitored so that developed protocols from these recommendations reflect the latest information.

Conclusion

This paper outlines general considerations and recommendations for dentists, oral health specialists, and craniomaxillofacial surgeons seeking to safely resume STSMs. These recommendations are designed to minimize the risk of exposure to COVID-19 by reinforcing social distancing protocols, reviewing criteria for patient and case selections, encouraging collaboration between organizations and local leadership, and team training. These guidelines should be tailored to fit the needs of each individual mission while keeping the safety as the main objective.

Modelling the SARS-CoV-2 outbreak: Assessing the usefulness of protective measures to reduce the pandemic at population level

A new bioinspired computational model was developed for the SARS-CoV-2 pandemic using the available epidemiological information, high-resolution population density data, travel patterns, and the average number of contacts between people. The effectiveness of control measures such as contact reduction measures, closure of communities (lockdown), protective measures (social distancing, face mask wearing, and hand hygiene), and vaccination were modelled to examine possibilities for control of the disease under several protective vaccination levels in the population. Lockdown and contact reduction measures only delay the spread of the virus in the population because it resumes its previous dynamics as soon as the restrictions are lifted. Nevertheless, these measures are probably useful to avoid hospitals being overwhelmed in the short term. Our model predicted that 56% of the Spanish population would have been infected and subsequently recovered over a 130 day period if no protective measures were taken but this percentage would have been only 34% if protective measures had been put in place. Moreover, this percentage would have been further reduced to 41.7, 27.7, and 13.3% if 25, 50 and 75% of the population had been vaccinated, respectively. Finally, this percentage would have been even lower at 25.5, 12.1 and 7.9% if 25, 50 and 75% of the population had been vaccinated in combination with the application of protective measures, respectively. Therefore, a combination of protective measures and vaccination would be highly efficacious in decreasing not only the number of those who become infected and subsequently recover, but also the number of people who die from infection, which falls from 0.41% of the population over a 130 day period without protective measures to 0.15, 0.08 and 0.06% if 25, 50 and 75% of the population had been vaccinated in combination with protective measures at the same time, respectively.

Just-in-Time Training for the Use of ICU Nurse Extenders During COVID-19 Pandemic Response

Landstuhl Regional Medical Center's response to the coronavirus disease 2019 pandemic included a plan to provide just-in-time training for nursing staff and paraprofessionals from throughout the organization in the event that it became overwhelmed with more critically ill patients than the facility was staffed to manage. Training conducted was a combination of online learning from the Society of Critical Care Medicine and the Association of Critical Care Nurses as well as a 2-hour block of hands-on skills. The three competencies for floating staff from Wright's Method for Competency Assessment were utilized in the training process, allowing trainees to (1) learn to fly, (2) market themselves in a positive way, and (3) understand crisis management options. Quick implementation of the plan led to over 125 nurses and paraprofessionals receiving the education and training in preparation for the pandemic response. The article further discusses training topics covered and the competency expectations for non-critical care nurses trained.

Machine learning spatio-temporal epidemiological model to evaluate Germany-county-level COVID-19 risk

As the COVID-19 pandemic continues to ravage the world, it is critical to assess the COVID-19 risk timely on multi-scale. To implement it and evaluate the public health policies, we develop a machine learning assisted framework to predict epidemic dynamics from the reported infection data. It contains a county-level spatio-temporal epidemiological model, which combines spatial cellular automata (CA) with time sensitive-undiagnosed-infected-removed (SUIR) model, and is compatible with the existing risk prediction models. The CA-SUIR model shows the multi-scale risk to the public and reveals the transmission modes of coronavirus in different scenarios. Through transfer learning, this new toolbox is used to predict the prevalence of multi-scale COVID-19 in all 412 counties in Germany. A t-day-ahead risk forecast as well as assessment of the non-pharmaceutical intervention policies is presented. We analyzed the situation at Christmas of 2020, and found that the most serious death toll could be 34.5. However, effective policy could control it below 21thousand, which provides a quantitative basis for evaluating the public policies implemented by the government. Such intervening evaluation process would help to improve public health policies and restart the economy appropriately in pandemics.

Assessment of effective mitigation and prediction of the spread of SARS-CoV-2 in Germany using demographic information and spatial resolution

Non-pharmaceutical interventions (NPIs) are important to mitigate the spread of infectious diseases as long as no vaccination or outstanding medical treatments are available. We assess the effectiveness of the sets of non-pharmaceutical interventions that were in place during the course of the Coronavirus disease 2019 (Covid-19) pandemic in Germany. Our results are based on hybrid models, combining SIR-type models on local scales with spatial resolution. In order to account for the age-dependence of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), we include realistic prepandemic and recently recorded contact patterns between age groups. The implementation of non-pharmaceutical interventions will occur on changed contact patterns, improved isolation, or reduced infectiousness when, e.g., wearing masks. In order to account for spatial heterogeneity, we use a graph approach and we include high-quality information on commuting activities combined with traveling information from social networks. The remaining uncertainty will be accounted for by a large number of randomized simulation runs. Based on the derived factors for the effectiveness of different non-pharmaceutical interventions over the past months, we provide different forecast scenarios for the upcoming time.

A pre-registered short-term forecasting study of COVID-19 in Germany and Poland during the second wave

Disease modelling has had considerable policy impact during the ongoing COVID-19 pandemic, and it is increasingly acknowledged that combining multiple models can improve the reliability of outputs. Here we report insights from ten weeks of collaborative short-term forecasting of COVID-19 in Germany and Poland (12 October-19 December 2020). The study period covers the onset of the second wave in both countries, with tightening non-pharmaceutical interventions (NPIs) and subsequently a decay (Poland) or plateau and renewed increase (Germany) in reported cases. Thirteen independent teams provided probabilistic real-time forecasts of COVID-19 cases and deaths. These were reported for lead times of one to four weeks, with evaluation focused on one- and two-week horizons, which are less affected by changing NPIs. Heterogeneity between forecasts was considerable both in terms of point predictions and forecast spread. Ensemble forecasts showed good relative performance, in particular in terms of coverage, but did not clearly dominate single-model predictions. The study was preregistered and will be followed up in future phases of the pandemic.

Data driven high resolution modeling and spatial analyses of the COVID-19 pandemic in Germany

The SARS-CoV-2 virus has spread around the world with over 100 million infections to date, and currently many countries are fighting the second wave of infections. With neither sufficient vaccination capacity nor effective medication, non-pharmaceutical interventions (NPIs) remain the measure of choice. However, NPIs place a great burden on society, the mental health of individuals, and economics. Therefore the cost/benefit ratio must be carefully balanced and a target-oriented small-scale implementation of these NPIs could help achieve this balance. To this end, we introduce a modified SEIRD-class compartment model and parametrize it locally for all 412 districts of Germany. The NPIs are modeled at district level by time varying contact rates. This high spatial resolution makes it possible to apply geostatistical methods to analyse the spatial patterns of the pandemic in Germany and to compare the results of different spatial resolutions. We find that the modified SEIRD model can successfully be fitted to the COVID-19 cases in German districts, states, and also nationwide. We propose the correlation length as a further measure, besides the weekly incidence rates, to describe the current situation of the epidemic.

Heterogeneity matters: Contact structure and individual variation shape epidemic dynamics

In the recent COVID-19 pandemic, mathematical modeling constitutes an important tool to evaluate the prospective effectiveness of non-pharmaceutical interventions (NPIs) and to guide policy-making. Most research is, however, centered around characterizing the epidemic based on point estimates like the average infectiousness or the average number of contacts. In this work, we use stochastic simulations to investigate the consequences of a population's heterogeneity regarding connectivity and individual viral load levels. Therefore, we translate a COVID-19 ODE model to a stochastic multi-agent system. We use contact networks to model complex interaction structures and a probabilistic infection rate to model individual viral load variation. We observe a large dependency of the dispersion and dynamical evolution on the population's heterogeneity that is not adequately captured by point estimates, for instance, used in ODE models. In particular, models that assume the same clinical and transmission parameters may lead to different conclusions, depending on different types of heterogeneity in the population. For instance, the existence of hubs in the contact network leads to an initial increase of dispersion and the effective reproduction number, but to a lower herd immunity threshold (HIT) compared to homogeneous populations or a population where the heterogeneity stems solely from individual infectivity variations.

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.

What Can We Learn from the Time Evolution of COVID-19 Epidemic in Slovenia?

A recent work indicates that temporarily splitting larger populations into smaller groups can efficiently mitigate the spread of SARS‐CoV‐2 virus. The fact that, soon afterward, the two million people Slovenia was the first European country proclaiming the end of COVID‐19 epidemic within national borders may be relevant from this perspective. Motivated by this evolution, in this paper the time dynamics of coronavirus cases in Slovenia is investigated with emphasis on how efficient various containment measures act to diminish the number of COVID‐19 infections. Noteworthily, the present analysis does not rely on any speculative theoretical assumption; it is solely based on raw epidemiological data. Out of the results presented here, the most important one is perhaps the finding that, while imposing drastic curfews and travel restrictions reduce the infection rate κ by a factor of four with respect to the unrestricted state, they only improve the κ‐value by ≈15% as compared to the much bearable state of social and economic life wherein wearing face masks and social distancing rules are enforced/followed. Significantly for behavioral and social science, our analysis may reveal an interesting self‐protection instinct of the population, which became manifest even before the official lockdown enforcement.

Non-pharmaceutical interventions during the COVID-19 pandemic: A review

Infectious diseases and human behavior are intertwined. On one side, our movements and interactions are the engines of transmission. On the other, the unfolding of viruses might induce changes to our daily activities. While intuitive, our understanding of such feedback loop is still limited. Before COVID-19 the literature on the subject was mainly theoretical and largely missed validation. The main issue was the lack of empirical data capturing behavioral change induced by diseases. Things have dramatically changed in 2020. Non-pharmaceutical interventions (NPIs) have been the key weapon against the SARS-CoV-2 virus and affected virtually any societal process. Travel bans, events cancellation, social distancing, curfews, and lockdowns have become unfortunately very familiar. The scale of the emergency, the ease of survey as well as crowdsourcing deployment guaranteed by the latest technology, several Data for Good programs developed by tech giants, major mobile phone providers, and other companies have allowed unprecedented access to data describing behavioral changes induced by the pandemic. Here, I review some of the vast literature written on the subject of NPIs during the COVID-19 pandemic. In doing so, I analyze 348 articles written by more than 2518 authors in the first 12 months of the emergency. While the large majority of the sample was obtained by querying PubMed, it includes also a hand-curated list. Considering the focus, and methodology I have classified the sample into seven main categories: epidemic models, surveys, comments/perspectives, papers aiming to quantify the effects of NPIs, reviews, articles using data proxies to measure NPIs, and publicly available datasets describing NPIs. I summarize the methodology, data used, findings of the articles in each category and provide an outlook highlighting future challenges as well as opportunities.

Fleeing lockdown and its impact on the size of epidemic outbreaks in the source and target regions - a COVID-19 lesson

The COVID-19 pandemic forced authorities worldwide to implement moderate to severe restrictions in order to slow down or suppress the spread of the disease. It has been observed in several countries that a significant number of people fled a city or a region just before strict lockdown measures were implemented. This behavior carries the risk of seeding a large number of infections all at once in regions with otherwise small number of cases. In this work, we investigate the effect of fleeing on the size of an epidemic outbreak in the region under lockdown, and also in the region of destination. We propose a mathematical model that is suitable to describe the spread of an infectious disease over multiple geographic regions. Our approach is flexible to characterize the transmission of different viruses. As an example, we consider the COVID-19 outbreak in Italy. Projection of different scenarios shows that (i) timely and stricter intervention could have significantly lowered the number of cumulative cases in Italy, and (ii) fleeing at the time of lockdown possibly played a minor role in the spread of the disease in the country.

Modelling the effectiveness of intervention strategies to control COVID-19 outbreaks and estimating healthcare demand in Germany

Objectives

An outbreak of the novel coronavirus in December 2019 caused a worldwide pandemic. This disease also impacts European countries, including Germany. Without effective medicines or vaccines, non-pharmaceutical interventions are the best strategy to reduce the number of cases.

Study design

A deterministic model was simulated to evaluate the number of infectious and healthcare demand.

Method

Using an age-structured SEIR model for the COVID-19 transmission, we project the COVID-19–associated demand for hospital and ICU beds within Germany. We estimated the effectiveness of different control measures, including active case-finding and quarantining of asymptomatic persons, self-isolation of people who had contact with an infectious person, and physical distancing, as well as a combination of these control measures.

Results

We found that contact tracing could reduce the peak of ICU beds as well as mass testing. The time delay between diagnosis and self-isolation influences the control measures. Physical distancing to limit the contact rate would delay the peak of the outbreak, which results in the demand for ICU beds being below the capacity during the early outbreak.

Conclusions

Our study analyzed several scenarios in order to provide policymakers that face the pandemic of COVID-19 with insights into the different measures available. We highlight that the individuals who have had contact with a virus-positive person must be quarantined as soon as possible to reduce contact with possible infectious cases and to reduce transmission. Keeping physical distance and having fewer contacts should be implemented to prevent overwhelming ICU demand.

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We developed an age-structured SEIR model for the COVID-19 to project the demand for hospital and ICU beds within Germany.

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The self-isolation of at-risk groups and mass testing have impacts on the peak of ICU beds.

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Physical distancing would delay the peak of outbreak.

The exposure risk to COVID-19 in most affected countries: A vulnerability assessment model

The world is facing the coronavirus pandemic (COVID-19), which began in China. By August 18, 2020, the United States, Brazil, and India were the most affected countries. Health infrastructure and socioeconomic vulnerabilities may be affecting the response capacities of these countries. We compared official indicators to identify which vulnerabilities better determined the exposure risk to COVID-19 in both the most and least affected countries. To achieve this purpose, we collected indicators from the Infectious Disease Vulnerability Index (IDVI), the World Health Organization (WHO), the World Bank, and the Brazilian Geography and Statistics Institute (IBGE). All indicators were normalized to facilitate comparisons. Speed, incidence, and population were used to identify the groups of countries with the highest and lowest risks of infection. Countries’ response capacities were determined based on socioeconomic, political, and health infrastructure conditions. Vulnerabilities were identified based on the indicator sensitivity. The highest-risk group included the U.S., Brazil, and India, whereas the lowest-risk group (with the largest population by continent) consisted of China, New Zealand, and Germany. The high-sensitivity cluster had 18 indicators (50% extra IDVI), such as merchandise trade, immunization, public services, maternal mortality, life expectancy at birth, hospital beds, GINI index, adolescent fertility, governance, political stability, transparency/corruption, industry, and water supply. The greatest vulnerability of the highest-risk group was related first to economic factors (merchandise trade), followed by public health (immunization), highlighting global dependence on Chinese trade, such as protective materials, equipment, and diagnostic tests. However, domestic political factors had more indicators, beginning with high sensitivity and followed by healthcare and economic conditions, which signified a lesser capacity to guide, coordinate, and supply the population with protective measures, such as social distancing.

[Nationwide exposure model for COVID-19 intensive care unit admission]

Hintergrund

Prognosemodelle zur Intensivbelegung mit COVID-19-Patienten sind in der aktuellen Pandemie wichtig zur strategischen Planung der Patientenallokation und Vermeidung regionaler Überlastung. Sie werden oft vollständig an retrospektiven Infektions- und Belegungsdaten trainiert, wodurch die Prognoseunsicherheit exponentiell mit dem Prognosehorizont anwachsen kann.

Methodik

Wir schlagen einen alternativen Modellansatz vor, bei dem das Modell weitgehend unabhängig von den zu simulierenden Belegungsdaten erstellt wird. Die Verteilung der Bettenbelegungen für Patientenkohorten wird direkt aus Belegungsdaten aus „Sentinel-Kliniken“ berechnet. Durch Kopplung mit Infektionsszenarien wird der Prognosefehler durch den Fehler der Infektionsdynamikszenarien beschränkt. Das Modell erlaubt eine systematische Simulation von beliebigen Infektionsszenarien, die Berechnung von Korridoren für die Bettenauslastung sowie Sensitivitätsanalysen im Hinblick auf Schutzmaßnahmen.

Ergebnisse

Das Modell wurde anhand von Klinikdaten und durch Anpassung von nur 2 Parametern an die Daten in der Städteregion Aachen und Deutschland gesamt vorgenommen.

Am Beispiel der Simulation der jeweiligen Bettenbelegungen für das Bundesgebiet wird das Belastungsmodell zur Berechnung von Belegungskorridoren demonstriert. Die Belegungskorridore bilden Schranken für die Bettenbelegungen für den Fall, dass die Infektionszahlen spezifische Grenzwerte nicht überschreiten. Darüber hinaus werden Lockdownszenarien simuliert, die sich an retrospektiven Ereignissen orientieren.

Diskussion

Unser Modell zeigt, dass eine deutliche Reduktion der Prognoseunsicherheit in Auslastungsprognosen durch gezielte Kombination von Daten aus unterschiedlichen Quellen möglich ist. Es erlaubt eine beliebige Kombination mit Modellen und Szenarien zur Infektionsdynamik und kann damit sowohl zur Belastungsprognose als auch für Sensitivitätsanalysen für zu erwartende neuartige Spreading- und Lockdownszenarien eingesetzt werden.

Zusatzmaterial online

Die Onlineversion dieses Beitrags (10.1007/s00063-021-00791-7) enthält die Simulation der Prognosekorridore der Intensivbettenbelegung für die Bundesländer. Beitrag und Zusatzmaterial stehen Ihnen auf www.springermedizin.de zur Verfügung. Bitte geben Sie dort den Beitragstitel in die Suche ein, das Zusatzmaterial finden Sie beim Beitrag unter „Ergänzende Inhalte“.

Market Stability Reserve under exogenous shock: The case of COVID-19 pandemic

The EU implemented the Market Stability Reserve (MSR) in response to the 2008 financial crisis to deal with short-term impacts of future shocks, such as the COVID-19 pandemic. We link a model that intertemporally optimizes the handling of banked allowances every five years with one that simulates the annual working of the EU ETS including the MSR with its potential cancelling. Neglecting the pandemic, 2.16 billion allowances are cancelled. Accounting for the pandemic, 0.28 billion additional allowances are cancelled if the European economy fully recovers by 2021, which even overcompensates the 2020 drop in CO2 emissions. Additional cancelling increases when the pandemics lasts longer, meaning that the MSR even outperforms its initial purpose. Thus, we conclude that no additional policy measures to support abatement are required in response to the COVID-19 pandemic.

A Proposed Epidemiologic Risk Threshold for SARS-CoV-2 for Assisting Healthcare Decision-Making

Introducción

La pandemia por SARS-CoV-2 es el mayor desafío sanitario en los últimos 100 años, ocasionando el mayor exceso de mortalidad no bélico en este período en el mundo occidental. Ante una enfermedad de elevada contagiosidad y asintomática en un tercio de los casos, es fundamental disponer de modelos que predigan su evolución. Pretendemos desarrollar un modelo de predicción de infección por COVID-19 en provincias españolas.

Método

Análisis de componentes principales funcional de datos epidemiológicos de las provincias españolas en función de su curva epidémica entre el 24 de febrero y el 8 de junio. Con este método se han clasificado las provincias en función de su evolución (peor, intermedia y mejor). Se han empleado los datos del Centro Nacional de Epidemiología.

Resultados

Se identificaron 2 componentes que explican el 99% de la variabilidad de las 52 curvas. La primera componente es la tendencia global de la tasa de incidencia, y la segunda componente es la velocidad de crecimiento o decrecimiento de la incidencia durante el período. Se identificaron 10 provincias en el grupo de peor evolución y 17 en el de evolución intermedia. Los valores umbrales de la tasa de incidencia a 7 días fueron 134 casos/100.000 habitantes para un nivel de alerta 1 (medio) y 167 para el nivel 2 (alto), consiguiendo un elevado poder de discriminación entre provincias.

Conclusiones

Estos niveles de alerta podrían ser de utilidad para decidir medidas que puedan afectar a la movilidad de la población, siempre y cuando haya una situación de transmisión comunitaria de SARS-CoV-2. Esta información sería intercomparable entre áreas sanitarias o comunidades autónomas.

Modelling personal cautiousness during the COVID-19 pandemic: a case study for Turkey and Italy

Although policy makers recommend or impose various standard measures, such as social distancing, movement restrictions, wearing face masks and washing hands, against the spread of the SARS-CoV-2 pandemic, individuals follow these measures with varying degrees of meticulousness, as the perceptions regarding the impending danger and the efficacy of the measures are not uniform within a population. In this paper, a compartmental mathematical model is presented that takes into account the importance of personal cautiousness (as evidenced, for example, by personal hygiene habits and carefully following the rules) during the COVID-19 pandemic. Two countries, Turkey and Italy, are studied in detail, as they share certain social commonalities by their Mediterranean cultural codes. A mathematical analysis of the model is performed to find the equilibria and their local stability, focusing on the transmission parameters and investigating the sensitivity with respect to the parameters. Focusing on the (assumed) viral exposure rate, possible scenarios for the spread of COVID-19 are examined by varying the viral exposure of incautious people to the environment. The presented results emphasize and quantify the importance of personal cautiousness in the spread of the disease.

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.

Optimal control and sensitivity analysis for transmission dynamics of Coronavirus

Analysis of mathematical models designed for COVID-19 results in several important outputs that may help stakeholders to answer disease control policy questions. A mathematical model for COVID-19 is developed and equilibrium points are shown to be locally and globally stable. Sensitivity analysis of the basic reproductive number (R₀) showed that the rate of transmission from asymptomatically infected cases to susceptible cases is the most sensitive parameter. Numerical simulation indicated that a 10% reduction of R₀ by reducing the most sensitive parameter results in a 24% reduction of the size of exposed cases. Optimal control analysis revealed that the optimal practice of combining all three (public health education, personal protective measure, and treating COVID-19 patients) intervention strategies or combination of any two of them leads to the required mitigation of transmission of the pandemic.