Development of the reproduction number from coronavirus SARS-CoV-2 case data in Germany and implications for political measures

Abstract Background SARS-CoV-2 has induced a worldwide pandemic and subsequent non-pharmaceutical interventions (NPIs) to control the spread of the virus. As in many countries, the SARS-CoV-2 pandemic in Germany has led to a consecutive roll-out of different NPIs. As these NPIs have (largely unknown) adverse effects, targeting them precisely and monitoring their effectiveness are essential. We developed a compartmental infection dynamics model with specific features of SARS-CoV-2 that allows daily estimation of a time-varying reproduction number and published this information openly since the beginning of April 2020. Here, we present the transmission dynamics in Germany over time to understand the effect of NPIs and allow adaptive forecasts of the epidemic progression. Methods We used a data-driven estimation of the evolution of the reproduction number for viral spreading in Germany as well as in all its federal states using our model. Using parameter estimates from literature and, alternatively, with parameters derived from a fit to the initial phase of COVID-19 spread in different regions of Italy, the model was optimized to fit data from the Robert Koch Institute. Results The time-varying reproduction number (Rt) in Germany decreased to <1 in early April 2020, 2–3 weeks after the implementation of NPIs. Partial release of NPIs both nationally and on federal state level correlated with moderate increases in Rt until August 2020. Implications of state-specific Rt on other states and on national level are characterized. Retrospective evaluation of the model shows excellent agreement with the data and usage of inpatient facilities well within the healthcare limit. While short-term predictions may work for a few weeks, long-term projections are complicated by unpredictable structural changes. Conclusions The estimated fraction of immunized population by August 2020 warns of a renewed outbreak upon release of measures. A low detection rate prolongs the delay reaching a low case incidence number upon release, showing the importance of an effective testing-quarantine strategy. We show that real-time monitoring of transmission dynamics is important to evaluate the extent of the outbreak, short-term projections for the burden on the healthcare system, and their response to policy changes.

Download Full-text

The Impact of the Climate Action Programme 2030 and Federal State Measures on the Uptake of Renewable Heating Systems in Lower Saxony’s Building Stock

Energies ◽

10.3390/en14092533 ◽

2021 ◽

Vol 14 (9) ◽

pp. 2533

Author(s):

Isabel Haase ◽

Herena Torio

Keyword(s):

Energy Demand ◽

National Level ◽

Policy Formulation ◽

Federal State ◽

Lower Saxony ◽

Building Stock ◽

Federal States ◽

Climate Action ◽

Action Programme ◽

The Impact

A heating transition is urgently needed to fulfil the national CO2 reduction targets in Germany. Thus, in 2019, there has been a strong policy push towards increasing the share of renewables in heating through the introduction of the Climate Action Programme 2030 and the reform of existing policies. In addition to the policy landscape on the national level, federal states have further leeway to implement policies; these options are currently largely unresearched. In order to fill this gap, we developed a System Dynamics Model for Lower Saxony to determine the effect of recent policy changes as well as additional regional subsidy schemes on the heating market. The results show that even though changes in subsidies can increase the renewable uptake considerably, the CO2e and energy demand reduction targets are not met in any of the examined scenarios. Furthermore, the model shows that policy formulation must take the inertia of the sector into account and completely turn away from fossil fuels to reach the stipulated emission reductions.

Download Full-text

Estimating the increase in reproduction number associated with the Delta variant using local area dynamics in England

10.1101/2021.11.30.21267056 ◽

2021 ◽

Author(s):

Sam Abbott ◽

Adam J. Kucharski ◽

Sebastian Funk ◽

Keyword(s):

Generation Time ◽

Reproduction Number ◽

National Level ◽

Specific Effect ◽

Local Area ◽

R Package ◽

Time Varying ◽

Local Authorities ◽

S Gene ◽

Real Time Analysis

AbstractBackgroundLocal estimates of the time-varying effective reproduction number (Rt) of COVID-19 in England became increasingly heterogeneous during April and May 2021. This may have been attributable to the spread of the Delta SARS-CoV-2 variant. This paper documents real-time analysis that aimed to investigate the association between changes in the proportion of positive cases that were S-gene positive, an indicator of the Delta variant against a background of the previously predominant Alpha variant, and the estimated time-varying Rt at the level of upper-tier local authorities (UTLA).MethodWe explored the relationship between the proportion of samples that were S-gene positive and the Rt of test-positive cases over time from the 23 February 2021 to the 25 May 2021. Effective reproduction numbers were estimated using the EpiNow2 R package independently for each local authority using two different estimates of the generation time. We then fit a range of regression models to estimate a multiplicative relationship between S-gene positivity and weekly mean Rt estimate.ResultsWe found evidence of an association between increased mean Rt estimates and the proportion of S-gene positives across all models evaluated with the magnitude of the effect increasing as model flexibility was decreased. Models that adjusted for either national level or NHS region level time-varying residuals were found to fit the data better, suggesting potential unexplained confounding.ConclusionsOur results indicated that even after adjusting for time-varying residuals between NHS regions, S-gene positivity was associated with an increase in the effective reproduction number of COVID-19. These findings were robust across a range of models and generation time assumptions, though the specific effect size was variable depending on the assumptions used. The lower bound of the estimated effect indicated that the reproduction number of Delta was above 1 in almost all local authorities throughout the period of investigation.

Download Full-text

Modeling COVID-19 Transmissions and Evaluation of Large Scale Social Restriction in Jakarta, Indonesia

10.1101/2020.10.30.20222984 ◽

2020 ◽

Author(s):

A. Hasan ◽

Y. Nasution ◽

H. Susanto ◽

E.R.M. Putri ◽

V.R. Tjahjono ◽

...

Keyword(s):

Quantitative Evaluation ◽

Large Scale ◽

Reproduction Number ◽

World Health ◽

Transmission Model ◽

Time Varying ◽

Short Term ◽

Social Restriction ◽

Short Term Forecasting ◽

Health Organization

AbstractThis paper presents mathematical modeling and quantitative evaluation of Large Scale Social Restriction (LSSR) in Jakarta between 10 April and 4 June 2020. The special capital region of Jakarta is the only province among 34 provinces in Indonesia with an average Testing Positivity Rate (TPR) below 5% recommended by the World Health Organization (WHO). The transmission model is based on a discrete-time compartmental epidemiological model incorporating suspected cases. The quantitative evaluation is measured based on the estimation of the time-varying effective reproduction number (ℛt). Our results show the LSSR has been successfully suppressed the spread of COVID-19 in Jakarta, which was indicated by ℛt < 1. However, once the LSSR was relaxed, the effective reproduction number increased significantly. The model is further used for short-term forecasting to mitigate the course of the pandemic.

Download Full-text

Norovirus transmission dynamics: a modelling review

Epidemiology and Infection ◽

10.1017/s0950268817002692 ◽

2017 ◽

Vol 146 (2) ◽

pp. 147-158 ◽

Cited By ~ 13

Author(s):

K. A. M. GAYTHORPE ◽

C. L. TROTTER ◽

B. LOPMAN ◽

M. STEELE ◽

A. J. K. CONLAN

Keyword(s):

Reproduction Number ◽

Population Level ◽

Transmission Dynamics ◽

Parameter Estimates ◽

Viral Gastroenteritis ◽

Recent Interest ◽

And Control ◽

Case Notification ◽

Substantial Morbidity ◽

Current Modelling

SUMMARYNorovirus is one of the leading causes of viral gastroenteritis worldwide and responsible for substantial morbidity, mortality and healthcare costs. To further understanding of the epidemiology and control of norovirus, there has been much recent interest in describing the transmission dynamics of norovirus through mathematical models. In this study, we review the current modelling approaches for norovirus transmission. We examine the data and methods used to estimate these models that vary structurally and parametrically between different epidemiological contexts. Many of the existing studies at population level have focused on the same case notification dataset, whereas models from outbreak settings are highly specific and difficult to generalise. In this review, we explore the consistency in the description of norovirus transmission dynamics and the robustness of parameter estimates between studies. In particular, we find that there is considerable variability in estimates of key parameters such as the basic reproduction number, which may mean that the effort required to control norovirus at the population level may currently be underestimated.

Download Full-text

Transmissibility of coronavirus disease 2019 (COVID-19) in Chinese cities with different transmission dynamics of imported cases

10.1101/2020.03.15.20036541 ◽

2020 ◽

Author(s):

Ka Chun Chong ◽

Wei Cheng ◽

Shi Zhao ◽

Feng Ling ◽

Kirran N. Mohammad ◽

...

Keyword(s):

Reproduction Number ◽

Likelihood Function ◽

Transmission Dynamics ◽

Time Varying ◽

Outbreak Response ◽

Chinese Cities ◽

Imported Cases ◽

Response Measures ◽

Local Transmission

AbstractBackgroundMonitoring the time-varying reproduction number (Rt) of the disease is useful in determining whether there is sustained transmission in a population. In this study, we examined Rt of COVID-19 and compared its transmissibility between different intervention periods in Hangzhou and Shenzhen.MethodsDaily aggregated counts of confirmed imported and local cases between January 1, 2020 and March 13, 2020 were analysed. A likelihood function was constructed to estimate Rt, accounting for imported cases.ResultsAlthough Hangzhou had fewer number of cases than Shenzhen, Shenzhen had higher proportion of imported cases than Hangzhou (83% vs 29%). Since the epidemic of COVID-19 in Shenzhen was dominated by imported cases, Rt was kept below unity through time. On the contrary, Rt was greater than unity in Hangzhou from 16 January to 7 February due to the surge in local cases. Credits to the Wuhan lockdown and outbreak response measures following the local lockdown, Rt decreased steadily and dropped below unity in mid-February.ConclusionThe lockdown measures and local outbreak responses helped reduce the potential of local transmission in Hangzhou and Shenzhen. Meanwhile, cities with similar epidemic trend could have different transmission dynamics given the variation in imported cases.

Download Full-text

Assessing the effects of time-dependent restrictions and control actions to flatten the curve of COVID-19 in Kazakhstan

PeerJ ◽

10.7717/peerj.10806 ◽

2021 ◽

Vol 9 ◽

pp. e10806

Author(s):

Ton Duc Do ◽

Meei Mei Gui ◽

Kok Yew Ng

Keyword(s):

Ad Hoc ◽

Reproduction Number ◽

National Level ◽

Control Measures ◽

Time Dependent ◽

Transmission Dynamics ◽

Model Parameters ◽

Real World Data ◽

Control Actions ◽

And Control

This article presents the assessment of time-dependent national-level restrictions and control actions and their effects in fighting the COVID-19 pandemic. By analysing the transmission dynamics during the first wave of COVID-19 in the country, the effectiveness of the various levels of control actions taken to flatten the curve can be better quantified and understood. This in turn can help the relevant authorities to better plan for and control the subsequent waves of the pandemic. To achieve this, a deterministic population model for the pandemic is firstly developed to take into consideration the time-dependent characteristics of the model parameters, especially on the ever-evolving value of the reproduction number, which is one of the critical measures used to describe the transmission dynamics of this pandemic. The reproduction number alongside other key parameters of the model can then be estimated by fitting the model to real-world data using numerical optimisation techniques or by inducing ad-hoc control actions as recorded in the news platforms. In this article, the model is verified using a case study based on the data from the first wave of COVID-19 in the Republic of Kazakhstan. The model is fitted to provide estimates for two settings in simulations; time-invariant and time-varying (with bounded constraints) parameters. Finally, some forecasts are made using four scenarios with time-dependent control measures so as to determine which would reflect on the actual situations better.

Download Full-text

National and state wise estimate of time varying reproduction number for COVID-19 in India during the nationwide lockdown

10.1101/2020.05.01.20087197 ◽

2020 ◽

Author(s):

Padmanaban Venkatesan

Keyword(s):

Programming Language ◽

Reproduction Number ◽

National Level ◽

Control Measures ◽

Effective Control ◽

Time Varying ◽

Epidemic Spread ◽

R Programming Language ◽

R Programming

AbstractTo understand the effect of nationwide lockdown on transmissibilty of SARS-CoV-2 in India, time varying reproduction number during the first weeks of April, 2020 was estimated. The time varying reproduction number was estimated using EpiEstim package in R programming language. The reproduction number has come down significantly during the lockdown period both at national level and in most states but it wasn’t reduced to less than 1. This calls for urgent need for more effective control measures in addition to lockdown to stop the epidemic spread of the virus.

Download Full-text

The Transition to Renewable Energy Technologies—Impact on Economic Performance of North Rhine-Westphalia

Applied Sciences ◽

10.3390/app9183783 ◽

2019 ◽

Vol 9 (18) ◽

pp. 3783 ◽

Cited By ~ 1

Author(s):

Gianmarco Aniello ◽

Johannes Többen ◽

Wilhelm Kuckshinrichs

Keyword(s):

Renewable Energy ◽

Power Plants ◽

Structural Changes ◽

Renewable Energy Sources ◽

National Level ◽

Energy Transition ◽

Energy System ◽

Production Costs ◽

Federal State ◽

Negative Effects

The economic impacts of the German Renewable Energy Act (EEG) are of considerable importance for the discussion of the energy transition in Germany (Energiewende). The Energiewende implies structural changes of the energy system by deploying Renewable Energy (and energy efficiency) Technologies (RET), but it also may induce structural changes for the overall economy, with uneven effects on a sub-national level. North-Rhine Westphalia (NRW) is an ideal case to study such regional disparities, since this federal state has scarce per-capita renewable energy sources, whereas it stands out for its energy intensive industry and fossil-fuel based power plants. In order to support renewable energy policies, mostly gross impact assessments of RET deployment have been carried out both on national and regional levels. By definition, such analyses result in positive assessments, since only expansionary effects resulting from additional demand for RET are accounted for. This paper, in contrast, presents a net impact assessment of the EEG on the NRW economy of both expansionary and contractionary effects. The latter consist of negative income effects, increased production costs and, the crowding-out of conventional energy due to the renewable energy financing mechanism (i.e., electricity surcharge), as well as its preferential status for feed-in. Our findings show how North-Rhine Westphalia, with regard to the operation of RET, suffers disproportionally from negative effects in relation to the value addition of its economy in comparison to the rest the country, whereas it benefits marginally from the production of such facilities.

Download Full-text

Transmission dynamics of COVID-19 in Ghana and the impact of public health interventions

10.1101/2021.07.04.21259991 ◽

2021 ◽

Author(s):

Sylvia K. Ofori ◽

Jessica S. Schwind ◽

Kelly L. Sullivan ◽

Benjamin J Cowling ◽

Gerardo Chowell ◽

...

Keyword(s):

Public Health ◽

Reproduction Number ◽

National Level ◽

Health Interventions ◽

Time Varying ◽

Public Health Interventions ◽

The Public ◽

Case Count ◽

Lower Case ◽

The Impact

The study characterized the transmission of COVID-19 in Ghana by estimating the time-varying reproduction number (Rt) and exploring the effect of various public health interventions at the national and regional levels. The median Rt for Ghana and six out of sixteen regions dropped from greater than 1 in March 2020 to less than 1 in September but increased above 1 in January 2021. The relaxation of movement restrictions and religious gatherings were not associated with increased Rt in the regions with lower case burdens. However, Rt increased in most regions after schools were reopened in January 2021. In a regression analysis, we estimated that the per-capita cumulative case count increased with population size. Findings indicated the public health interventions reduced the Rt at the national level while at the regional levels, the Rt fluctuated, and the extent of fluctuation varied across regions.

Download Full-text

Transmission Dynamics and Short-Term Forecasts of COVID-19: Nepal 2020/2021

Epidemiologia ◽

10.3390/epidemiologia2040043 ◽

2021 ◽

Vol 2 (4) ◽

pp. 639-659

Author(s):

Sushma Dahal ◽

Ruiyan Luo ◽

Raj Kumar Subedi ◽

Meghnath Dhimal ◽

Gerardo Chowell

Keyword(s):

Performance Metrics ◽

Growth Models ◽

National Level ◽

Growth Parameter ◽

Transmission Dynamics ◽

Short Term ◽

Linear Pattern ◽

Mobility Data ◽

Using Data ◽

Second Wave

Nepal was hard hit by a second wave of COVID-19 from April–May 2021. We investigated the transmission dynamics of COVID-19 at the national and provincial levels by using data on laboratory-confirmed RT-PCR positive cases from the official national situation reports. We performed 8 week-to-week sequential forecasts of 10-days and 20-days at national level using three dynamic phenomenological growth models from 5 March 2021–22 May 2021. We also estimated effective and instantaneous reproduction numbers at national and provincial levels using established methods and evaluated the mobility trends using Google’s mobility data. Our forecast estimates indicated a declining trend of COVID-19 cases in Nepal as of June 2021. Sub-epidemic and Richards models provided reasonable short-term projections of COVID-19 cases based on standard performance metrics. There was a linear pattern in the trajectory of COVID-19 incidence during the first wave (deceleration of growth parameter (p) = 0.41–0.43, reproduction number (Rt) at 1.1 (95% CI: 1.1, 1.2)), and a sub-exponential growth pattern in the second wave (p = 0.61 (95% CI: 0.58, 0.64)) and Rt at 1.3 (95% CI: 1.3, 1.3)). Across provinces, Rt ranged from 1.2 to 1.5 during the early growth phase of the second wave. The instantaneous Rt fluctuated around 1.0 since January 2021 indicating well sustained transmission. The peak in mobility across different areas coincided with an increasing incidence trend of COVID-19. In conclusion, we found that the sub-epidemic and Richards models yielded reasonable short-terms projections of the COVID-19 trajectory in Nepal, which are useful for healthcare utilization planning.

Download Full-text