Could Madrid’s perimeter lockdown strategy have worked?

By Dr. Alfonso de Miguel Arribas, ZLC Researcher.

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During the Covid pandemic, most urban areas around the world adopted a range of  ‘non pharmaceutical interventions’ or NPIs, from compulsory mask-wearing and sanitation to lockdowns which aim to curtail the spread of the virus by amongst other things reducing the mobility of citizens.

From September 2020 to May 2021, (the second and third waves of the pandemic) Madrid (and, independently, Santiago de Chile), employed an unusual variant of this strategy known as perimeter lockdown (PL). Several statistical studies have suggested that this strategy was largely ineffective. We have tried to go beyond analysing the outcome in Madrid’s particular circumstances by attempting a mechanistic model which, while informed by data from Madrid, is generalised and may reveal whether, in other conditions and perhaps implemented in different ways, a PL strategy could nonetheless be an effective tool in an epidemic situation.

As we all now know, and was recognised by the authorities in Madrid at the time, blanket lockdowns and quarantines have devastating economic and societal consequences. It was therefore quite reasonable to seek a more fine-grained approach which would specifically target those neighbourhoods particularly affected by the virus while allowing the rest of the conurbation to continue to operate rather more normally. Based on cumulative incidence data being gathered at the level of Basic Health Zones, where this showed the greatest cause for concern mobility in and out of the BHZ was restricted, but elsewhere in the city residents were able to go to work or school, perform other essential activities and use public transport while small businesses were allowed to open, albeit at reduced capacity.

Basically, PLs were enforced in areas where the 14-day cumulative incidence rate (CIR) of infection was above a certain threshold (although thresholds changed as the pandemic evolved). However, health data shows that the timings of changes in CIR mean they cannot be attributed to the application of PLs, and further that cumulative incidence rate increases and decreases were highly synchronised across all BHZs, whether these were subject to PL restrictions or not. That is the basis for claims that the PL strategy was largely ineffective.

We are then able to look at data on mobility. Here we can use data gathered by the Ministry of Transport, derived from cell phone records which of course track the movements of phones, and therefore their owners, between the areas served by different masts (although note that this data doesn’t fully resolve to the BHZ level, but it gives a fairly good assessment of trends in mobility). We were able to look at figures for a typical pre-pandemic week, at the situation during the first, national, lockdown (March – June 2020), and for most of the period covered by Madrid’s PL strategy.

Broadly, the national lockdown reduced mobility to 40% of the ‘normal’ baseline and as restrictions were eased during the summer of 2020 this rose back up to 70%. August being holiday season, the figure then dropped to 50% of baseline but was back up to 70% by late September when the PL strategy was implemented.

And during PL? Averaged over the period, mobility levels across the city remained at 63%, or 67% excluding weekends. It is fair to say, then, that the overall impact of PLs on citywide mobility (which, recall, was assumed to be an important vector for the spread of the disease) was negligible.

That is what actually happened. Were other outcomes for a PL strategy possible? Our generalised model has a metapopulation (a collection of sub-populations in administrative districts that can exchange individuals who, infected in one subpopulation, may travel to another and start an infection there). We modelled mobility in an origin-destination matrix based on real, pre-pandemic, mobility data. We assumed a range of general mitigation measures, such as face-mask wearing, were in place, and we used an ‘effective reproduction number’ and infectious period length as estimated by the Ministry of Health when the ‘second wave’ started.

We also had to include a ‘risk threshold’ which defines when PL will be applied to an area, and a factor to reflect that PL was not the only intervention in these high risk areas.

Running our simulations, we were looking for three epidemiological observables: overall peak incidence, final prevalence, and the final proportion of districts that had exceeded the given risk threshold at some point. We can compare these against an entirely unmitigated scenario, as we vary three free parameters – general mobility, risk threshold, and transmissibility reduction.

Our modelling showed that reducing general mobility could indeed help reduce the impact of the epidemic, but there is a problem. To achieve more than a fairly negligible effect, the risk thresholds that trigger PL would have to be drastically lower than those actually employed in Madrid, and mobility an order of magnitude lower than that achieved during the national lockdown. With a much more strict threshold for PL we could reduce peak incidence by more than 20% and prevalence by around 10%, but unless mobility were reduced by 90% or more, so many areas would be subject to PL that the result is a de facto general lockdown – which is what PL was intended to avoid.

We can run the model another way, with mobility maintained but greater reductions in transmissibility. However, since we assume that other NPIs are already in place, this may not be achievable, and in any case even very significant reductions in peak incidence and prevalence would still leave all areas of the city experiencing some outbreaks above the risk threshold. So while PL could in these conditions greatly reduce the impact on the population, it wouldn’t protect parts of the city from the most affected areas under even mild epidemiological conditions.

Meanwhile, running the model even with very low threshold values, only a strong reduction in mobility will protect from invasion of the entire system.

Our work adds to that of others in questioning both the proper implementation and the effectiveness of the Madrid experience. Others have already noted that decreases in the epidemic curve started before PL implementations could have been effective and that the strategy didn’t increase the rate at which cases declined. It is also suggested that emphasis on reducing mobility rather than preventing high risk situations was misguided, and given the amount of ‘essential’ travel (emergency services, health care, basic supplies) still required that reduction may not be achievable. (It is also worth noting that, even during PL periods it was still permissible to travel to work in another district). These points agree well with our own modelling. There is also the observation that basing PLs on BHZs may not be effective, since these zones are essentially administratively defined and have little reality ‘on the ground’ for citizens.

In summary, the tightest criterion for imposing PL on a district had a 14-day CIR value of 500 (cases per every 100,000 inhabitants): to have a significant effect, this value should have been more like 20 (which might not be perceptible ‘in real time’) and mobility reductions would have to be greater than those achieved even during the fairly draconian national lockdown. Bear in mind also that our model assumed much tighter restrictions on PLs than were the case in practice so could in many ways be regarded as a ‘best case’ scenario.

Perimeter lockdowns therefore appear to be an inefficient response to an epidemic of this nature at the urban scale due to the high interconnectedness of such systems. Nonetheless there are unanswered questions. Both the strategy, and our modelling, assume a degree of homogeneity in the way that populations mix which may not be true at smaller scale. The effects of lockdowns and indeed of other non-pharmaceutical interventions may vary across different socio-economic groups, and it is indeed possible that, beyond the initial stages of an outbreak, mobility in itself may play only a relatively minor role.

The full paper is available at https://www.nature.com/articles/s41598-023-31614-8

For more information, please see our paper (reference above) or contact Alfonso de Miguel Arribas, ademiguel@zlc.edu.es.