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Facts Interpretations

Modeling Covid-19 U.K. fatalities

Abstract

Two models of the Covid-19 U.K. epidemics were calibrated respectively on offical death data and on an estimate of total excess death for 2020. We demonstrate the U.K. was in an unfavorable initial position with R0 around 3, higher than most countries. The effect of social distancing and decision of lockdown was positive, saving an astonishing 300,000 lives. The predicted death toll on 1st August is 61,500 at least. We show that should the lockdown have been implemented a week earlier, 24,000 lives would have been saved, length of epidemics and strain on hospitals drastically reduced.

Methodology

We follow similar methodology as published in previous articles, using model previously described. Our CovModel 1.6 SIR model is calibrated to historical death curve by varying the R factor with time. This way, we obtain an insight on social distancing and policy measures. In this article, we matched two models on two sources of data to 28 April 2020.

MODEL 1. Death curve obtained from Johns Hopkins University CSSE repository at https://github.com/CSSEGISandData. There, data provided by the U.K. government are supposed to reflect direct deaths from Sars-CoV-2 infection.

MODEL 2. Death curve maintained and provided to us by Chris Giles on https://twitter.com/ChrisGiles_ . Chris is Economics Editor at the Finantial Times and his bio can be consulted on the newspaper’s website https://www.ft.com/chris-giles. His work provides an estimate of the net excess death incidence in the U.K., that is the deaths directly or indirectly caused by the Covid-19 epidemics in the spring 2020 outbreak.

Results

Figures 1 and 2 provide detailed results respectively for Model 1 and 2.

R factor

Both models provide a similar estimate of R factor history in the U.K.

R0 is around 3, a high value compared to other countries we studied (France , Italy, China , South Korea, Iceland ).

The first occurrence of social distancing behaviour happened around February 24 to 26, as shown by R factor reducing to around 2. (For information, on February 25, government decided that certain traveller from outbreak regions would be isolated.)

R factor then only significantly decreases next around March 7 to 11 (R=1.35 to 1.5). (For information, the U.K. leaved the “contain” phase of March 12).

Significant reduction in R, below 1, happens between March 19 and 26. (For information, the U.K. entered into lockdown on Monday 23 March).

The consistency of results demonstrates the viability of SIR methods matched to death curve to evaluate R factor.

Death forecast

Model 1 predicts 40,800 direct deaths on August, 1 2020. Model 2 predicts 61,500 total deaths.

Based on statistics as of April 28, the ratio of total over direct deaths is 2.08 to 1. By applying this ratio to Model 1 direct death forecast, we estimate Model 1 predicts 81,600 total deaths on August, 1.

The two methods gives us a range of total expected direct and indirect deaths in the U.K. from the first “spring” outbreak of the disease between 60,000 and 81,600 on August,1 2020.

Immunity

Assuming infection provides total and durable immunity (which may not be guaranteed), the level of acquired group immunity is low according to our model: the immunisation threshold is 67% but only 6 to 12% were infected. Note that model may have limitations to address this, since no age class were modelled and the differential susceptibility of population may not be fully captured in model. In addition, vast uncertainties remain in the Infection Fatality Ratio (IFR) globally (IFR is an assumption of model, linking modelled infections to the simulated death curve). We estimated very different values of the IFR accross countries, even wondering if the epidemics was really “one” in the whole world, if various strains of the virus may not result in different clinical patterns.

The worrying low level of predicted immunity and uncertainties in the IFR are, again, strong incentives to carry intensive serology surveys NOW in the U.K.

Figure 1: Model 1 calibrated on official death count.
Figure 2: Model 2 calibrated on Chris Giles total direct and indirect deaths

Effect of lockdown decision on reducing death toll

We used Model 2 for this sensitivity, since the purpose is to assess the effect on total fatalities.

By assuming a value of R = 1.35 from March,7 until June,1 it is estimated death toll would have been 374,000, meaning collective lockdown saved more than 300,000 lives. Figure 3 illustrates.

Figure 3. Predicted total death toll from Model 2 if lockdown had not taken place.

Effect of delay in implementing lockdown

There are two ways to address this question. The first is to assume lockdown could reasonably have occurred a week earlier if the U.K. government had followed decisions made by the majority of fellow countries at the time. This is illustrated in Figure 4. The second is to assume a lockdown and severe social distancing could have occurred as early as beginning of March, based on decisions taken in rare countries, and in a hypothetical situation of very alternative political decisions were taken. This is illustrated and commented in Figure 5.

Both sensitivities are explicit that delays in implementing strict social distancing, and/or contact tracing and testing measures as in Iceland, have resulted in 24,000 to 40,000 extra deaths and caused a longer epidemics outbreak with no chance to suppress the virus in the short term.

Figure 4: effect of lockdown decision a week earlier. Model 2. Death toll on August, 1st: 37,169 or 24,000 less than actual.

Figure 5: effect of early lockdown decision on 1st March. Model 2. Death toll on August, 1st: 21,409 or 40,000 less than actual.

Effect of ending lockdown on May, 15

A simple sensitivity on Model 1 shows easing lockdown too early would result in epidemics relapse. The rate of resurgence will depend on R factor. We show here the effect of R=1.2.

Figure 6: Model 1. Ending lockdown with R = 1.2 on 15 May results in death incidence increase with two to three weeks dealy and a resurgence of epidemics

Conclusion: the importance of quality death time series

Our preference is to model direct death occurrences as in Model 1. This is because infection proportion are more directly linked to death data accounted according to this standard. For example, the IFR significance is altered in Model 2. The internal consistency of CovModel and SIR models is better when calibrated on death occurences directly related to the infection. Forecasts obtained from Model 1 and Model 2 significantly differ (even after correcting Model 1 for total deaths). The quality and accuracy of death records is important to a science point of view because it impacts the quality of models and our ability to fight the epidemics. We very much regret that such poor records were maintained in many developed countries including the U.K. and France.

Acknowledgment

To Chris Giles, Economics editor at the Financial Times, for having passed on to us his data in a useful tabulated format. We are very grateful for his collaboration and would like to congratulate him for his investigative work on the epidemics.

Photo by Yoss Cinematic from Pexels