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

abstract_fig.png


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

fig1.png fig3.png

Fig. 1. Inference of central epidemiological parameters

of the SIR model during the initial onset period,

2 to 15 March 2020.


tab2.png



=


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



Model-based_and_model-free_characterization_of_epidemic_outbreaks.full_fig11.png

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


figS2_small.png


new infections (number / day) = Screen shot 2021-02-06 at 09.37.07.png

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)

tabS1.png


Results

Deutschland

figS5a.png



figS6.png

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


figS4b.png figS5c.png


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)


newfig1.png


fig2.png

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.

  1. The equilibrium value ooNobs increases with weaker contact reduction kt or higher influx Φt. No equilibrium is reached, if either kt or Φt are above the respective (critical) threshold values.
  2. The critical value ktcrit represents the minimal contact reduction that is required to reach equilibrium and stabilise case numbers. If case numbers are below the TTI capacity limit, lower values of ktcrit are required for stabilisation (blue) than if cases exceed TTI (grey). Confidence intervals originate from error propagation of the uncertainty of the underlying model parameters.
  3. (c–f) In the unstable dynamic regime (kt = 20%), a tipping point is visible when exceeding TTI capacity.



newfig3.png

Figure 3:

(a - c) The effectiveness of a lockdown depends on 3 main parameters:

  1. its duration, reference: 4 weeks
  2. stringency (strength: kLD = 75 %), and
  3. starting time: 4 weeks after exceeding TTI capacity.


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.



fig4.png


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:

  • We assumed that spreading happens homogeneously in the population, with neither regional nor age-related differences. In reality, heterogeneous spreading can lead to regionally differing case numbers, which illustrates the need for regional monitoring of the remaining test-trace-and-isolate (TTI) capacity to allow for early and targeted control measures.
  • In our scenarios, we further assumed that the behaviour of the population and subsequent contact reduction is constant over time (except during lockdown). Real situations are more dynamic, necessitating frequent reevaluations of the current restrictions and mitigation measures.
  • We also assumed a constant effectiveness of test-trace-and-isolate (TTI) if below the capacity limit, but if case numbers are very low, all the available test- and trace-efforts could be concentrated on the remaining infection chains. This would further facilitate a control at low case numbers.

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:

  • Fast testing,
  • rigorous isolation, and
  • a large proportion of traced contacts are essential.

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])