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Challenges in control of Covid-19: short doubling time and long delay to effect of interventions

Lorenzo Pellis, Francesca Scarabel, Helena B. Stage, Christopher E. Overton, Lauren H. K. Chappell, Katrina A. Lythgoe, Elizabeth Fearon, Emma Bennett, Jacob Curran-Sebastian, Rajenki Das, Martyn Fyles, Hugo Lewkowicz, Xiaoxi Pang, Bindu Vekaria, Luke Webb, Thomas House, Ian Hall

arXiv:2004.00117v1q-bio.PE

TL;DR

Early COVID-19 growth-rate estimates were uncertain, and reproduction-number estimates relied on limited or setting-specific evidence. The authors estimate growth and infection-to-detection delays from European data, finding rapid doubling and a lag between interventions and visible effects that matters for control decisions.

  • Problem

    COVID-19 R0 estimates varied widely and often drew on early Wuhan or Diamond Princess data, limiting the evidence available for planning interventions across different populations.

    Source: §1 · p. 2

  • Method

    The authors estimate growth rates across multiple countries and methods, and assess incubation and symptom-onset-to-hospitalisation delays across settings.

    Source: §2 · pp. 2–3

  • Results

    About 3 days or less was the doubling time in most studied European countries before mitigation, and new-case drops appeared 8–9 days after initial measures in the UK and Italy.

    Source: §2 · pp. 3–4

  • Takeaways & Limitations

    Short doubling times and long detection delays can leave observed cases far below the epidemic's underlying extent, so case counts and R0 alone can underestimate the intervention required.

    Source: §3 · p. 5

    Reporting errors, case-definition changes, and testing-regime shifts could bias estimates, although the authors argue these are unlikely to explain the consistent fast-growth pattern across countries.

    Source: §2 · p. 3

Abstract

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Early assessments of the spreading rate of COVID-19 were subject to significant uncertainty, as expected with limited data and difficulties in case ascertainment, but more reliable inferences can now be made. Here, we estimate from European data that COVID-19 cases are expected to double initially every three days, until social distancing interventions slow this growth, and that the impact of such measures is typically only seen nine days - i.e. three doubling times - after their implementation. We argue that such temporal patterns are more critical than precise estimates of the basic reproduction number for initiating interventions. This observation has particular implications for the low- and middle-income countries currently in the early stages of their local epidemics.

1. Introduction

Early COVID-19 intervention planning faced uncertain reproduction-number estimates based largely on limited, setting-specific outbreaks. The authors argue that directly observable epidemic growth and infection-to-detection delays are more relevant to deciding when control action is urgent.

1. Introduction

  • Early, aggressive lockdowns in India and South Africa began at relatively low reported case counts, potentially improving containment chances but carrying substantial social and personal costs.India had 434 confirmed cases and zero deaths when its nationwide lockdown was declared; South Africa had 927 known cases and zero deaths at the start of its 21-day lockdown.Source: §1 · p. 2
  • 1.4–6.49 is the reported range of COVID-19 R0 estimates, while most official sources settle at 2–3.Differences reflect methods, model structures, parameter values, and data sources; early estimates relied heavily on Wuhan and the Diamond Princess, with limited or potentially biased data and distinctive settings.Source: §1 · p. 2
  • R0 estimates should be updated using more numerous and reliable data from outbreaks worldwide, since estimates in one population may not translate to another.Source: §1 · p. 2
  • Growth speed and infection-to-detection delay are more relevant to implementing COVID-19 controls than precise R0 estimates.The authors note that doubling times can be estimated directly from data and delay estimates are relatively consistent, so sophisticated models are not required to infer urgency.Source: §1 · p. 2

2. Results

Across European outbreaks, cases grew rapidly before mitigation, while infection-to-detection and intervention-to-observed-effect delays left several days of growth unobserved. The authors also find that R0 estimates are assumption-sensitive and provide limited guidance on intervention intensity or timing.

Epidemic growth

  • About 3 days or less was the doubling time found across most studied European countries before mitigation, using two methods and multiple indicators.The analyses included confirmed cases across countries and hospitalisations, ICU admissions, and deaths in Italy; conclusions were similar despite differing confidence intervals and matched visual log-scale inspection.Source: §2 · p. 3

Robustness and limitations

  • Reporting errors, case-definition changes, or testing-regime shifts could mislead estimates, but the authors conclude that evidence for fast exponential growth without intervention is overwhelming.They argue that fast growth and high counts make small biases less consequential, constant underreporting does not change the trend, and faster growth is difficult to produce consistently across countries through temporary changes in ascertainment.Source: §2 · p. 3

Delays to detection

  • At least 9 days separated mean incubation and mean symptom-onset-to-hospitalisation times in every setting except Singapore, or about 3 doubling times.The authors' estimates accounted for truncated observations and exponential case growth, and were consistent with the literature while showing geographical variation.Source: §2 · p. 4

Intervention effects

  • 8–9 days after initial, relatively soft measures, new-case counts visibly dropped in both the UK and Italy.In the UK, cases continued growing exponentially for 9 days after the first measure, with daily confirmed cases rising approximately 8-fold; household transmission and later reporting of hospitalisations and deaths add further delays.Source: §2 · p. 4

R0 estimates

  • For a growth rate of 0.25/day, estimated R0 values ranged from 2 to 4 or larger, depending strongly on assumptions about pre-symptomatic transmission.The assumed amount of pre-symptomatic transmission varies widely across the literature.Source: §2 · p. 4

R0 and control

  • R0 offers limited guidance on the required intervention: examples require stopping 75% of transmission when R0 is four, versus 50% when R0 is two.The latter example assumes most transmission is pre-symptomatic and would require socially disruptive measures such as quarantining apparently healthy people; R0 also does not indicate how quickly interventions should begin.Source: §2 · pp. 4–5

3. Discussion

The discussion warns that short doubling times and long detection delays can leave observed cases far behind the underlying epidemic. It argues for swift action, particularly where healthcare capacity is low, while noting the analysis's data-access boundary.

3. Discussion

  • At unconstrained growth, doubling local hospital capacity buys only 3 days before bed capacity is breached, while observed-case-based strategies can underestimate the intervention needed.The authors emphasize this concern for low- and middle-income countries with apparently low case counts, and say that in settings with low healthcare capacity and common intergenerational mixing, swift action will save numerous lives.Source: §3 · p. 5
  • The authors advocate stronger action by national and international health communities, especially to support low- and middle-income countries early in their epidemics.They connect the concern to low healthcare capacity and common intergenerational mixing in those settings.Source: §3 · p. 5

Data availability

  • The analysis data and code are available in a GitHub repository, except for UK onset-to-hospitalisation delay data that cannot be shared under a data-sharing agreement.Source: §3 · p. 5

Parameter Mean Standard deviation

Supplementary analyses estimate epidemic growth and event delays across datasets, then examine how modeling assumptions shape R0 inferences. They report short delays and growth times, while showing that R0 estimates are sensitive to assumptions with limited data support.

  • The authors estimate growth with quasi-Poisson GLMs for clear exponential-growth windows and GAMs that allow time-varying local growth rates and doubling times.The GAM’s extrapolation is not sensible for forecasting, and its smoother may create boundary effects.Source: Parameter Mean Standard deviation · p. 15
  • Among 15 countries, several showed transitions from short to longer doubling times, while others showed constant or oscillatory patterns.Belgium and Romania had equivalent GAM and GLM fits; Germany, the Netherlands and the UK showed more oscillatory doubling times.Source: Parameter Mean Standard deviation · pp. 15–16, Figure S1 · p. 18
  • Delay estimation must correct for right truncation and exponential epidemic growth, which otherwise over-represent short observed delays near the sampling endpoint.The analysis uses a conditional likelihood for observing the second event before the final sampling date.Source: Estimating delay distributions · p. 16
  • Incubation averaged 4.84 days (standard deviation 2.79), while onset-to-hospitalisation averaged 5.14 days in the UK, 4.41 in Hong Kong, and 2.62 in Singapore.The UK delay estimate used 106 cases; the incubation estimate used 162 cases.Source: Estimating delay distributions · p. 16
  • For a growth rate of 0.25 day−1, close to that observed in Italy and the UK, R0 estimates were highly sensitive to small variations in poorly supported quantities and generally larger, possibly much larger, than official estimates.Source: Estimation of R0 · p. 17
  • A simple SEIR model produced much smaller R0 estimates, whereas assumed individual infectiousness variability or 50% fully asymptomatic cases did not significantly change estimates.Source: Estimation of R0 · p. 17
  • R0 calculations assume mass-action mixing and vary infectivity timing; the authors note that social structure may matter more as R0 approaches 1.Their explored infectivity profiles vary the assumed start of the infectious period and use mean durations of 2 or 3 days.Source: Estimation of R0 · p. 17
  • A visual check across cases, hospitalisations and deaths found broadly fast growth, but Italy’s cases and hospitalisations slowed before deaths did.The comparison used eyeballed exponential guide lines, not statistical fits.Source: Parameter Mean Standard deviation · p. 16, Figure S3 · p. 20
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