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

Khailaie, Sahamoddin; Mitra, Tanmay; Bandyopadhyay, Arnab; Schips, Marta; Mascheroni, Pietro; Vanella, Patrizio; Lange, Berit; Binder, Sebastian; Meyer‐Hermann, Michael

doi:10.1101/2020.04.04.20053637

Cited by 70 publications

(169 citation statements)

References 36 publications

(48 reference statements)

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“…7b). This is in accordance with recent modeling studies [22], which suggest that the effective reproduction number R ≈ 1 as of April 2, meaning that the disease free equilibrium is on the verge of instability (cf. Fig.…”

Section: Ld Partial Economic and Social Activitiessupporting

confidence: 93%

“…6a). This matches with estimations of the RKI [31] and findings by other groups which are also currently studying the situation in Germany [9,22]. This naturally results in a significant uncertainty of the projection since small deviations of the parameters can make the difference between further growing active case numbers or slowly declining numbers.…”

Section: Ld Partial Economic and Social Activitiessupporting

confidence: 87%

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The impact of current and future control measures on the spread of COVID-19 in Germany

Barbarossa

Fuhrmann

Meinke

et al. 2020

Preprint

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The novel coronavirus (SARS-CoV-2), identified in China at the end of December 2019 and causing the disease COVID-19, has meanwhile led to outbreaks all over the globe with about 2.2 million confirmed cases and more than 150,000 deaths as of April 17, 2020 [37]. In view of most recent information on testing activity [32], we present here an update of our initial work [4]. In this work, mathematical models have been developed to study the spread of COVID-19 among the population in Germany and to asses the impact of non-pharmaceutical interventions. Systems of differential equations of SEIR type are extended here to account for undetected infections, as well as for stages of infections and age groups. The models are calibrated on data until April 5, data from April 6 to 14 are used for model validation. We simulate different possible strategies for the mitigation of the current outbreak, slowing down the spread of the virus and thus reducing the peak in daily diagnosed cases, the demand for hospitalization or intensive care units admissions, and eventually the number of fatalities. Our results suggest that a partial (and gradual) lifting of introduced control measures could soon be possible if accompanied by further increased testing activity, strict isolation of detected cases and reduced contact to risk groups.

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Section: Ld Partial Economic and Social Activitiessupporting

confidence: 93%

Section: Ld Partial Economic and Social Activitiessupporting

confidence: 87%

The impact of current and future control measures on the spread of COVID-19 in Germany

Barbarossa

Fuhrmann

Meinke

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…At initial time point t 0 , for our model S = 1; further assuming κ U = 1 and κ I = 1, we note that Equation 18 boils down to R 0 = β γ which agrees with the standard SIR model. The basic reproduction number R 0 can be generalized over time to obtain time dependent reproduction number R t that represents can be interpreted as the expected number of secondary cases produced by a single infection in a completely susceptible population at some time point t during the pandemic [4]. We can further extend Equation 18, to compute R t :…”

Section: Methodsmentioning

confidence: 99%

“…The basic reproduction number R 0 is defined as the expected number of secondary cases produced by a single infection in a completely susceptible population during the initial phase of the pandemic [4]. We follow the next generation matrix method for calculating the R 0 value of our SUIR model [6].…”

Section: Appendixmentioning

confidence: 99%

The timing of contact restrictions and pro-active testing balances the socio-economic impact of a lockdown with the control of infections

Bej

2020

Preprint

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During the SARS-CoV-2 pandemic, numerous mathematical models have been developed. Reporting artefacts and missing data about asymptomatic spreaders, imply considerable margins of uncertainty for model-based predictions. Epidemiological models can however also be used to investigate the consequences of measures to control the pandemic, reflected in changes to parameter values.We present a SIR-based, SUIR model in which the influence of testing and a reduction of contacts is studied by distinguishing 'Unidentified' and 'Identified' spreaders of infections. The model uses four ordinary differential equations and is kept deliberately simple to investigate general patterns occurring from testing and contact restrictions. The model goes beyond other efforts, by introducing time dependent parameter curves that represent different strategies in controlling the pandemic.Our analysis reveals the effect of 'pro-active' testing for the design of contact restriction measures. By pro-active testing we mean testing beyond those people who show symptoms. The simulations can explain why the timing of contract restrictions and pro-active testing is important. The model can also be used to study the consequence of different strategies to exit from lockdown.Our SUIR model is implemented in Python and is made available through a Juypter Notebooks. This an extensive documentation of the derivation and implementation of the model, as well as transparent and reproducible simulation studies. Our model should contribute to a better understanding of the role of testing and contact restrictions.

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“…2. We use the same compartments and transition-types but simplify the notation compared to [25] to make the intuitive meaning of the variables clearer 3 . We denote the compartments by C = {S, E, C, I, H, U, R, D}, where each node can be susceptible(S), exposed (E), a carrier (C), infected (I), hospitalized (H), in the (intensive care unit (U), dead (D), or recovered (R).…”

Section: A Network-based Covid-19 Spreading Modelmentioning

confidence: 99%

Importance of Interaction Structure and Stochasticity for Epidemic Spreading: A COVID-19 Case Study

Großmann

Backenköhler

Wolf

2020

Preprint

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In the recent COVID-19 pandemic, computer simulations are used to predict the evolution of the virus propagation and to evaluate the prospective effectiveness of non-pharmaceutical interventions. As such, the corresponding mathematical models and their simulations are central tools to guide political decision-making. Typically, ODE-based models are considered, in which fractions of infected and healthy individuals change deterministically and continuously over time.In this work, we translate an ODE-based COVID-19 spreading model from literature to a stochastic multi-agent system and use a contact network to mimic complex interaction structures. We observe a large dependency of the epidemic's dynamics on the structure of the underlying contact graph, which is not adequately captured by existing ODEmodels. For instance, existence of super-spreaders leads to a higher infection peak but a lower death toll compared to interaction structures without super-spreaders. Overall, we observe that the interaction structure has a crucial impact on the spreading dynamics, which exceeds the effects of other parameters such as the basic reproduction number R0. We conclude that deterministic models fitted to COVID-19 outbreak data have limited predictive power or may even lead to wrong conclusions while stochastic models taking interaction structure into account offer different and probably more realistic epidemiological insights.

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

Cited by 70 publications

References 36 publications

The impact of current and future control measures on the spread of COVID-19 in Germany

The impact of current and future control measures on the spread of COVID-19 in Germany

The timing of contact restrictions and pro-active testing balances the socio-economic impact of a lockdown with the control of infections

Importance of Interaction Structure and Stochasticity for Epidemic Spreading: A COVID-19 Case Study

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