Derivation of the effective reproduction number ℛ for COVID-19 in relation to mobility restrictions and confinement

Arenas, Àlex; Cota, Wesley; Gómez‐Gardeñes, Jesús; Gómez, Sergio; Granell, Clara; Matamalas, Joan T.; Soriano‐Paños, David; Steinegger, Benjamin

doi:10.1101/2020.04.06.20054320

Cited by 36 publications

(39 citation statements)

References 31 publications

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“…More detailed models using SIR-like descriptions for metapopulations and adding mobility usually incorporate uncertainty in their predictions. In this way, ranges for different quantities have been derived, such as for the basic reproductive number

and its temporal response to confinement measures ( 34 ), for the number of undocumented infected individuals ( 14 ) or estimations of the effect of physical-distancing measures in the median number of infections ( 11 ).…”

Section: Discussionmentioning

confidence: 99%

The turning point and end of an expanding epidemic cannot be precisely forecast

Castro

Ares

Cuesta

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

144

120

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Epidemic spread is characterized by exponentially growing dynamics, which are intrinsically unpredictable. The time at which the growth in the number of infected individuals halts and starts decreasing cannot be calculated with certainty before the turning point is actually attained; neither can the end of the epidemic after the turning point. A susceptible–infected–removed (SIR) model with confinement (SCIR) illustrates how lockdown measures inhibit infection spread only above a threshold that we calculate. The existence of that threshold has major effects in predictability: A Bayesian fit to the COVID-19 pandemic in Spain shows that a slowdown in the number of newly infected individuals during the expansion phase allows one to infer neither the precise position of the maximum nor whether the measures taken will bring the propagation to the inhibition regime. There is a short horizon for reliable prediction, followed by a dispersion of the possible trajectories that grows extremely fast. The impossibility to predict in the midterm is not due to wrong or incomplete data, since it persists in error-free, synthetically produced datasets and does not necessarily improve by using larger datasets. Our study warns against precise forecasts of the evolution of epidemics based on mean-field, effective, or phenomenological models and supports that only probabilities of different outcomes can be confidently given.

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Section: Discussionmentioning

confidence: 99%

The turning point and end of an expanding epidemic cannot be precisely forecast

Castro

Ares

Cuesta

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

144

120

View full text Add to dashboard Cite

show abstract

“…The constant reproduction number in Figure 1, left, nicely captures the exponential increase at the early stages of the outbreak, but fails to "bend the curve" before herd immunity occurs. Nonetheless, several recent studies have successfully used an SEIR model with a constant reproduction number to model the outbreak dynamics of COVID-19 in China [35] and in Europe [28] by explicitly reducing the total population N to an affected population N * = η N. The scaling coefficient η = N * /N is essentially a fitting parameter that indirectly quantifies the level of confinement [3]. For example, when averaged over 30 Chinese provinces, the mean affected population was η = 5.19 · 10 −5 ± 2.23 ± 10 −4 , suggesting that the effect of COVID-19 was confined to only a very small fraction of the total population [35].…”

Section: The Time-varying Effective Reproduction Number Reflects Thementioning

confidence: 99%

The reproduction number of COVID-19 and its correlation with public health interventions

Linka

Peirlinck

Kuhl

2020

Preprint

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Throughout the past four months, no number has dominated the public media more persistently than the reproduction number of COVID-19. This powerful but simple concept is widely used by the public media, scientists, and political decision makers to explain and justify political strategies to control the COVID-19 pandemic. Here we explore the effectiveness of political interventions using the reproduction number of COVID-19 across Europe. We propose a dynamic SEIR epidemiology model with a time-varying reproduction number, which we identify using machine learning and uncertainty quantification. During the early outbreak, the reproduction number was 4.5±21.4, with maximum values of 6.5 and 5.9 in Spain and France. As of today, it has dropped to 0.7±20.2, with minimum values of 0.4 and 0.3 in Austria and France. We found a strong correlation between passenger air travel and the reproduction number with a time delay of 12.6±22.7 days. Our new dynamic SEIR model provides the flexibility to simulate various outbreak control and exit strategies to inform political decision making and identify safe solutions in the benefit of global health.

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“…To date, studies of the country-specific progression of the COVID-19 pandemic 7 have mostly explored the independent effects of a single category of interventions. These categories include travel restrictions 2,8 , social distancing [9][10][11][12] and personal protective measures 13 . Additionally, modelling studies typically focus on NPIs that directly influence contact probabilities (for example, social distancing measures 18 , social distancing behaviours 12 , self-isolation, school closures, bans on public events 20 and so on).…”

mentioning

confidence: 99%