my excerpt of
Inferring change points in the spread of COVID-19 reveals the effectiveness of interventions
Jonas Dehning, Johannes Zierenberg, F. Paul Spitzner, Michael Wibral, Joao Pinheiro Neto, Michael Wilczek, Viola Priesemann
Science 369, 160 (2020)
10 July 2020
results
Die wellenförmige Bewegung der daily new cases wird durch lockdowns (an den tatsächlichen "change points" 1, 2, 3 und zu späteren Zeitpunkten) verursacht. |
model parameters
Fig. 1. Inference of central epidemiological parameters of the SIR model during the initial onset period, 2 to 15 March 2020.
Mean[λ0] = 0.45 / day, 90% CI = 1.6 σ = 0.8 / day |
my excerpt of
Model-based and model-free characterization of epidemic outbreaks
Jonas Dehning, F. Paul Spitzner, Matthias C. Linden, Sebastian B. Mohr, Joao Pinheiro Neto, Johannes Zierenberg, Michael Wibral, Michael Wilczek, and Viola Priesemann
16 September, 2020
Daily values are taken from situation reports [21, 23, 24] (full dataset) and the epi bulletin [22, 25] (ARS dataset). Weekly values, represented as horizontal lines, are taken from a situation report table and a weekly lab surveillance report (ARS dataset). Note: the latter represents a subset of all tests. Compared to the situation report, the ARS dataset lists weeks 8 to 10 individually. C: Overlay of Panel B with the number of cases reported per day by the RKI and the estimated epi curve
(imputation and Nowcasting, as described in [19] ). The fraction of positive tests correlates with the number of reported cases from week 13 onward, as the total number of tests reaches a constant level.
Sources of data
[19] M. an der Heiden and O. Hamouda. Schätzung der aktuellen Entwicklung der SARS-CoV-2-Epidemie in Deutschland – Nowcasting. Epidemiologisches Bulletin, 2020(17):10–15, 2020.
[21] Daily RKI situation report from Mai 25 https://www.rki. de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/ Situationsberichte/2020-05-27-en.pdf, 2020.
[22] SARS CoV2 Surveillance - Weekly report from May 26, 2020.
[23] Daily RKI situation report from April 8 https://www.rki. de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/ Situationsberichte/2020-04-08-en.pdf, 2020.
[24] Daily RKI situation report from Mai 5 https://www.rki. de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/ Situationsberichte/2020-05-22-de.pdf, 2020.
[21] Daily RKI situation report from Mai 25 https://www.rki. de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/ Situationsberichte/2020-05-27-en.pdf, 2020.
[22] SARS CoV2 Surveillance - Weekly report from May 26, 2020.
[23] Daily RKI situation report from April 8 https://www.rki. de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/ Situationsberichte/2020-04-08-en.pdf, 2020.
[24] Daily RKI situation report from Mai 5 https://www.rki. de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/ Situationsberichte/2020-05-22-de.pdf, 2020.
[25] A. Hoffmann, I. Noll, N. Willrich, A. Reuss, M. Feig, M.J. Schneider, T. Eckmanns, O. Hamouda, and M. Abu Sin. Laborbasierte Surveillance SARS-CoV-2. Epidemiologis- ches Bulletin, 2020(15):5–9, 2020.
[26] J. Seifried and O. Hamouda. Erfassung der SARS-CoV-2 Testzahlen in Deutschland. Epidemiologisches Bulletin, 2020(15):3–4, 2020.
my excerpt of
Low case numbers enable long-term stable pandemic control without lockdowns
Sebastian Contreras, Jonas Dehning, Sebastian B. Mohr, F. Paul Spitzner, and Viola Priesemann*
Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany.
Department of Physics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany.
10 December 2020
Model
new infections (number / day) = with γ R0 = &lambda0 = daily growth rate (transition coefficient S -> E) Rt = (1 − kt) Ro S/M = (1 - kt) λ0 / γ S/M with kt (%) = reduction of infectious contacts relative to pre-CoVID-19 times (%) HIT = 1 - 1/Rt (herd immunity threshold) |
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Results Deutschland
Supplementary Figure S6: Comparison of the reproduction number and reported cases as second wave emerges in different European countries. For each country, parameters of an SIR model were fitted to the reported data of the Our World in Data repository44, following the procedure presented in 18. (Panels X1) The time-dependent effective growth rate stays between −0.1 and 0.1 and rises before the tipping point. This corresponds to an effective reproduction number between 0.7 and 1.3, which matches our preliminary assumptions. The time range is adjusted to focus on the tipping point. (Panels X2) After a (meta-)stable regime in summer, all of the selected countries show a rise in case numbers and a tipping point at around 50 new cases per day per million, where the spread self-accelerates and the cases increase significantly. (Insets) Case numbers for the full available time range. References 18: Dehning, J. et al. Inferring change points in the spread of COVID-19 reveals the effectiveness of interventions. Science (2020) 44: Max Roser, E. O.-O., Hannah Ritchie & Hasell, J. Coronavirus pandemic (covid-19). Our World in Data (2020). https://ourworldindata.org/coronavirus, (Europe, America, and Oceania and Asia) |
Model parameters
mu (recovery rate) is called gamma in Figure S2 and Table S1 (in the row above) lambda o has not relation to the lambdas in Table S1 (above) |
Stability through contact reduction and test-trace-isolate (TTI)
Figure 2: (a, b) In the stable and metastable regimes, daily new cases approach an equilibrium value Nˆobs that depends on contact reduction kt and external influx of new cases Φt.
Figure 3:
(a - c) The effectiveness of a lockdown depends on 3 main parameters:
Observed daily new cases for a lockdown (abbreviated as LD) which is enacted after the TTI capacity has been exceeded. Reference parameters are a lockdown duration of 4 weeks, contact reduction during lockdown of kLD = 75 % and a start time at 4 weeks after exceeding TTI capacity. We vary lockdown duration (a), lockdown strength (b) and lockdown starting time (c) to investigate whether stable case numbers can be reached.
(d–f) Total cases after 3 months, if the lockdown is parameterised as described in panels a–c, respectively.
(g, h:) The minimal required duration of lockdown to reach equilibrium depends both on strength and start time.
Figure 4: On a long-term perspective, recurrent lockdowns are not required if the subsequent contact reduction knLD is sufficient to reach equilibrium.
A two-week lockdown of default strength (knLD = 75%) is either enacted when
Fig.4
Discussion ... In order to focus our model on the general spreading dynamics, we made simplifying assumptions:
Overall, our analytical results describe the general behaviour across countries well and identify the relevant factors for the control of the pandemic.
Quantitatively, our assumptions regarding the efficiency of test-trace-and-isolate (TTI) are in agreement with those of other modelling studies. ... test-trace-and-isolate (TTI) measures are an important contribution for the control of the pandemic but typically do not suffice alone. Their success strongly depends on their implementation:
Given our informed assumptions about these parameters, our model shows that contact reduction and test-trace-isolate (TTI) can only compensate a basic reproduction number R0 of 3.3, if contagious contacts are also reduced by about 40 % (95% CI: [24,53]) |