C-19: More on lock-downs (Part II)

Updated: May 11

This article is Part II of a previous article published on the subject of lock-downs due to COVID-19. We further explore data from Apple's COVID-19 Mobility report to glean useful insights that can help better predict the virus' infection trajectory, and help inform decisions on interventions that may be more or less effective.

#analytics #COVID


TL;DR version

  • Isolation, social distancing, and in effect, entirely inhibiting mobility is by far the single most effective way to taper COVID-19 infections. This may be stating the obvious, but the 'data-fit' to empirically derived transmission data is remarkably good

  • While these tactics work; none seem to be the definitive article or silver bullet, as projections suggest these factors alone fail to reduce transmission rates to <1. Rigorous testing (coupled with track, trace and isolate), as well as education, personal hygiene and other such precautionary measures likely make up the remaining taper required

  • Based on shift patterns in mobility vs. trajectory of infections, we observe that some countries got very unlucky with timing. While almost all lockdowns outside of Italy occurred during week 2 to 3 of March, at this point, some countries already had infections in the order of 50-100,000 persons, while for some others this was as low as 100. We think a large part of the issue here was an over-reliance on formally reported case detection data which gave a highly misleading view of the reality of the virus' spread in the population. For those countries with high infections, containment even with lock-downs was a major challenge and deaths mounted

  • The timing embedded within mobility reports has been used to ascertain the median time between infection and deaths; this is estimated to be ~10 days. This is an alarmingly low figure, and underscores the need to protect the elderly and vulnerable as the virus continues to spread


Before going deeper, the following chart tells us a lot

  • Firstly, to explain the chart; the x-axis represent deaths as at today (17 April), and the y-axis represents COVID-19 infections at point of lock-down (defined as the date at which mobility drops to 50% vs baseline levels - the dates vary between 14 to 23 March). Each point on the chart represents one country's data; and the two colours represent (1) detected case figures reported by authorities [blue], and (2) theoretical infection estimates obtained by using our death data-fitting method [red]

  • The testing error is clearly systematic throughout the entire range; demarcated by the fact that the two regression lines form a linear fit (in the log space). Also, the test error increases with larger infections, as the two regression lines diverge with larger figures. It is important for the reader to note, as this is the log space, that difference is also an exponential one

  • A key takeaway here is: the lock-down date is one of the strongest, if not the strongest determinant of death outcome for each country. A strong correlation is noted between the number of infections at point of lock-down (est. 14-23 March for all countries), and total deaths today (as at 17 April) - the correlation is consistent for both detected cases and modelled infections within R^2 > 0.75

  • Two more, no less important takeaways are: (1) under-testing most likely gave countries a wrong impression of the reality of their respective situations - the difference between the red and blue lines is significant, and (2) it made no sense for all countries to time their lock-downs to coincide, given the different stages of maturity, yet they did - all countries locked down between 14 and 23 March; which means, regretfully, that somehow solidarity was an important consideration for leaders to push forward on the agenda


Introduction & discussion. Refer to data in table & figures further below.

  1. Apple, like Google has made available location information to the public in a bid to help authorities monitor the impact of the on-going lock-down efforts due to COVID-19. Apple in particular utilises their Maps service data for this purposes, and the data is updated daily at a T-2 day lag

  2. It should be noted that Apple Maps is not very widely used in most countries as most smartphone users opt to use services such as Google Maps and Waze for navigation. As such, this data may not be a fully comprehensive and in Apple's own words, 'it may not be representative of the overall population'. With this caveat in mind, we feel the information is still valuable to explore a possible correlation between mobility and COVID-19 infections and death

  3. We have extracted this data here for analysis - in doing so, we have had to smooth out weekly seasonality due to weekend spikes, otherwise the data is as delivered by Apple

  4. Based on the datasets shown in the figures below it should be fairly obvious how complicated it is to correlate mobility data of a vast number of people, with how this factor translates to infection growth, via person-to-person transmission of the COVID-19 virus. Either dataset is voluminous, erratic and discontinuous, may likely be prone to errors in reporting, and subject to a multitude of factors outside of this study. It is also appropriate to mention here that developing a correlative link, however 'robust', does not necessarily mean it is a causal one.

  5. To improve the fit between the two datasets, we have utilised a theoretical model to fit the COVID-19 reported data; and used that as a go-between to match/fit the mobility information gleaned from Apple's reports. The results are promising, albeit riddled with ill-fitting least-square regressions and (one too many) layers of data smoothing

  6. We found that the onset of taper in transmission factor can be made to coincide with that of a pronounced reduction in mobility, via a time shift of 10-11 days; notwithstanding potential error propagation from assuming the median time between case detection and death at 8 days. We thus term this as the true median time lag between contracting the COVID-19 infection and death; this is found to be in good agreement with data from some 5 countries studied

  7. This figure, at 10 days, is an alarming one if indeed true. For reference, the median time for onset of symptoms to ICU admission discovered from observing patients of COVID-19 in Hubei province was measured at some 10 days (see here). This however was from observation of a finite number of just 41 patients admitted into hospital and subsequently sent to the ICU as their complications escalated. Such a short time span from contraction to death is unimaginable and perhaps highlights yet another highly sinister point about the disease, particularly its lethal effect to those with co-morbidities and are therefore predisposed to higher order complications from COVID-19 (e.g. respiratory problems, hypertension, diabetes etc.)

  8. In investigating the potential correlation between mobility and transmission factor, we found a reasonably good linear fit for the tapering section of these respective datasets with R^2 :0.97-0.99 for all mobility types. While all reduction in mobilities should correlate to transmission declines, we found that changes in transit mobility in general has the highest gradient to transmission factor (by a slim but visible margin); though we should caveat that no two cities operate the same way and as such this may well be very unique from country to country

  9. It is unfortunate to see that very few regressions suggest the ability to reduce transmission factor to <1 by making changes to mobility alone (see table below), i.e. transmission of the virus will continue to grow exponentially even if mobility (based on data indicated by Apple Maps) is reduced to zero across all mobility types; walking, transit and driving

  10. As we observe the changes in mobility across countries during the course of the last 4-6 weeks, it is rather clear that herd mentality existed. While Italian cities Rome and Milan reduced mobility towards end Feb/early March nearly all other cities showed a distinctly reduced mobility at onset dates between 14 to 23 March

  11. It is also heartening to see that a few countries had in fact reduced mobility dramatically, in spite of not yet having a formal lock-down policy in place. Countries such as Vietnam, Thailand, South Korea namely; and even Japan and Netherlands to a smaller extent. It seems wisdom of crowds truly does exist when it comes to people and communities protecting their own lives, even at the expense of their livelihoods

  12. This observed herding around a similar 'lock-down date window' was in spite the fact that all these countries were at very different stages of their COVID-19 developments. And to make matters worse, under-testing and delayed testing meant ALL countries were underestimating their infection figures, particularly those at the upper end of the scale - a recipe for disaster given high exponential growth of the virus. For example; UK reported 2,700 cases detected on 19 Mar (coinciding with its 50% mobility threshold point), however our model estimates some 80,000 infections were present at this point; for the US using New York's mobility threshold at 18 Mar, it reported 7,800 cases, whereas our model estimates were 100,000; and for Germany at a transition date of 16 Mar, it reported 7,300 with our model estimates at 14,000. As the reader can probably expect, such errors can easily translate to some very bad decisions; deaths in the UK and US have reached 13,000 and 32,000 respectively, while Germany to date has recorded 4,000 [all as at 17 April 2020]. As an additional comparison, the Philippines and Thailand, at transition date 15 Mar; correspondingly reported 140 cases detected vs 370 estimated, and 100 cases detected vs 100 estimated respectively. Clearly, there was a wide difference in the state of affairs of each country which may have not factored into how each country detailed out their lock-down plans. The strategy of lock-downs was simple and clear enough - shut down practically everything as quickly as possible

  13. In short, and perhaps a rather justified over-simplification - 'no other strategy mattered more to avert COVID-19 deaths than to have been lucky; that is, lucky enough to have had locked-down when every other country was, while infections were still at a manageably low figure'. For more than half of the world's countries, this was indeed the case; whereas for the largest economies in the world (perhaps due to transmission from international visitors and tourists) they weren't so lucky. Perhaps, for once, being a smaller economic power in the world is an advantage


Table: Summarised results of regression fit between COVID-19 deaths and changes in mobility during taper phase across a number of countries

  • Reasonable strong impact of transit mobility on virus spread, though in the case of Germany driving has the stronger contribution (max correlation gradient)

  • With exception of Germany, mobility changes alone are not expected to reduce transmission significantly to <1

  • Where appropriate mobility changes in a representative city are used instead of entire country, e.g. Sao Paolo for Brazil, and New York for the US. This is where the epicentres are for each country

  • Model deteriorates for deaths <100 as fewer gradations available given the number of data points


Figure 1: 'Walking' mobility changes for selected major cities around the world (Feb-April 2020) - added 17 April 2020

  • Almost all major cities have effectively 'locked-down' as they face COVID-19 (officially or unofficially); based on mobility changes, to a similar extent to one another

  • Lock-down timing across all cities fall within the range of 14-23 March 2020 to reach 50% mobility; with exception of Rome, Milan, Seoul, Tokyo and Stockholm

  • As we elaborated previously, the impact of the pandemic in terms of infections and death were very different from country to country at this point of transition

  • Key questions arise: (1) given the coinciding timing, did heard mentality play a role in how decision makers decided when to lock-down?, (2) were some countries simply unluckier than others to have been at a different state of evolution of the pandemic when the transition happened?


Reference figures

(A) Mobility data vs. modelled daily infection & deaths for various countries

  • Mobility data is indexed to 100% from arbitrary baseline date at mid February; assumed mortality rate is 1.2% for all countries, and 'delay' of 8 days between deaths and infections

  • For some countries, lock-downs were too little too late. Having reached cumulative infections of the order 50-100,000 locked downs did little to stop deaths from happening. In this category are the UK, US, France, Italy and Spain

  • For other countries, for example those in Asia such as Malaysia, Indonesia, Philippines and Thailand, lock-downs happened when infection figures were very low (<1,000), leading to a highly positive outcome as infection growth was stemmed early

  • Note; we use model infection figures here in lieu of reported case detection figures, as the latter is under-reported by at least a factor of 5-20 times in most instances; we have elaborated on this method in our early report here. From this point onwards, we will include mobility data in our future daily reports to continuously track this metric over time



(B) Country specific data for regression of mobility vs. transmission factor. Notes:

  • Top left: Country death data up to 14 April 2020 + model fitting using theoretical transmission factors <> provides theoretical model for death bell-curve

  • Top right: Mobility data, based on Apple COVID-19 Mobility report (driving, transit or walking) <> contains timing and magnitude information of changes to mobility due to partial/full lock-downs

  • Bottom right: Computed transmission factor based on actual death statistics + transmission factor model fits <> provides visual 'fit' of the transmission factor evolution over time

  • Bottom left: Linear curve fitting of decline section between transmission factor model fit and mobility data <> provides theoretical trajectory of transmission factors should mobility continue to be reduced to zero [given by the Y-axis intercept]


Germany: daily death data vs. mobility (driving)


Germany: daily death data vs. mobility (transit/public transport)


US: daily death data vs. mobility (transit/public transport) [New York mobility data]


US: daily death data vs. mobility (walking) [New York mobility data]


Indonesia: daily death data vs. mobility (walking)


Belgium: daily death data vs. mobility (transit/public transport)


Brazil: daily death data vs. mobility (transit/public transport) [Sao Paolo mobility data]


Italy: daily death data vs. mobility (transit/public transport)


Italy: daily death data vs. mobility (walking)


India: daily death data vs. mobility (walking)


Malaysia: daily death data vs. mobility (walking)





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