key: cord-0897968-1mlg35oo
authors: Galanis, G.; Di Guilmi, C.; Bennett, D. L.; Baskozos, G.
title: The effectiveness of Non Pharmaceutical Interventions in reducing the outcomes of the COVID-19 epidemic in the UK, an observational and modelling study.
date: 2020-12-16
journal: nan
DOI: 10.1101/2020.12.16.20248308
sha: e7ba3377ab18abe5414467222bfd5803c3386bdb
doc_id: 897968
cord_uid: 1mlg35oo

Epidemiological models used to inform government policies aimed to contain the contagion of COVID-19, assume that the reproduction rate is reduced through Non-Pharmaceutical Interventions (NPIs) leading to physical distancing. Available data in the UK show an increase in physical distancing before the NPIs were implemented and a fall soon after implementation. We aimed to estimate the effect of people's behaviour on the epidemic curve and the effect of NPIs taking into account this behavioural component. We have estimated the effects of confirmed daily cases on physical distancing and we used this insight to design a bevavioural SEIR model (BeSEIR), simulated different scenaria regarding NPIs and compared the results to the standard SEIR. Taking into account behavioural insights improves the description of the contagion dynamics of the epidemic significantly. The BeSEIR predictions regarding the number of infections without NPIs were several orders of magnitude less than the SEIR. However, the BeSEIR prediction showed that early measures would still have an important influence in the reduction of infections. The BeSEIR model shows that even with no intervention the percentage of the cumulative infections within a year will not be enough for the epidemic to resolve due to a herd immunity effect. On the other hand, a standard SEIR model significantly overestimates the effectiveness of measures. Without taking into account the behavioural component the epidemic is predicted to be resolved much sooner than when taking it into account.

The spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus responsible for COVID-19 has led to more than 9,277,214 confirmed cases and more than 478,691 deaths as of 25/06/020 [1] . Apart from the health-related implications, COVID-19 has been affecting almost every aspect of people's lives and these effects have been unequally distributed. [2] Given the current absence of a vaccine, governments have resorted to health policies known as Non-Pharmaceutical Interventions (NPIs), which are aimed to reduce the average number of contacts between individuals (physical distancing). A number of studies have explored the effects of NPIs on the contagion dynamics of COVID-19. [3] [4] [5] [6] One of the key focuses of compartmental epidemiological models used is the estimation of the effects of NPIs on the rate of spread of the epidemic, which is captured by the basic reproduction number initially and the effective one later. Hence, the effectiveness of the different policies depends on how the various announced measures reduce this parameter. In order to be able to capture the level of this effect, it is necessary to estimate the value of the effective reproduction number, which in standard compartmental models is assumed to be initially constant and to change as a response to NPIs. [7] However, data which capture mobility levels of individuals show that in a number of countries, including the UK, people reduced the number of visits and duration of stays (which are related to physical distancing practices) before the NPIs are made and in excess of these measures.

This behaviour, fits well with a number of epidemiological models, which take into account behavioural changes over and above NPIs [8] [9] [10] hence the effective reproduction becomes (at . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted December 16, 2020. ; https://doi.org/10.1101/2020.12.16.20248308 doi: medRxiv preprint least partly) endogenous. However, these works are theoretical and have not been applied to data sets related to COVID-19 so far.

The purpose of our study was threefold: (i) assess the influence of NPIs on physical distancing in the UK, taking into account individual behaviour due to observed cases; (ii) extend the standard SEIR model in order to incorporate individual behaviour using the analysis from (i); and (iii) use this extended model to study the effectiveness of the NPIs, including the level and timing of measures taken and the possible effects of lifting the measures.

In order to assess the influence of both NPIs and the observed information, we analysed the correlation between individuals' mobility levels and the number of daily confirmed cases of the previous day as reported in the WHO dashboard implemented by John Hopkins University, [1] for three different periods: (a) up to the point when advice for physical distancing and avoidance of unnecessary interactions and travel was given (b) between this advice and enforceable lockdown, and (c) after lockdown. Enforceable lockdown includes NPIs ranging from the closure of public spaces, transportation hubs and shops to forbidding interactions with people outside one's household and ban any unnecessary travel.

Following Buckee et al. (2020) , [11] we created an aggregated data time series for physical . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted December 16, 2020. ; https://doi.org/10.1101/2020.12.16.20248308 doi: medRxiv preprint distancing in the UK using data from Google's "COVID-19 Community Mobility Reports", which shows the changes in mobility in six different categories:

1. Retail and recreation, reporting the mobility trends for places such as restaurants, cafés, shopping centres, theme parks, museums, libraries and cinemas.

2. Supermarket and pharmacy, capturing the trends for places such as supermarkets, food warehouses, farmers markets, specialty food shops and pharmacies 3. Parks, which shows the mobility trends for places like national parks, public beaches, marinas, dog parks, plazas and public gardens. 4 . Public transport, which shows the mobility trends for places that are public transport hubs, such as underground, bus and train stations. 5. Workplaces, capturing mobility trends to places of work 6. Residential, which shows mobility trends for places of residence.

We noted that not all of the above categories are relevant for measuring levels of physical distancing, which on one hand are related to both NPIs and to individuals' behaviour, while on the other are relevant for the contagion dynamics. For this reason, we used the categories "Workplaces", "Public transport", "Retail and recreation". We defined as mobility ݉ ௧ mobility at time ‫ݐ‬ , a weighted average of these three mobility categories. In order to calculate the different weights, we first matched these categories with the relevant ones from the national travel survey, 2018 [12] which includes the following travel categories: Business, Education, Escort education, Shopping, Personal Business, Visiting friends at private home, Visiting friends elsewhere, Entertainment / public activity, Sport, Holiday, Day trip, Other.

We matched the National Travel Survey categories "Holiday", "Day trip", "Entertainment / public activity", "Shopping", "Visiting friends elsewhere (than home)" to the "Retail and Recreation" mobility trend; "Commuting", "Business" and "Personal Business" to the "Workplaces" mobility . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted December 16, 2020. ; https://doi.org/10.1101/2020.12.16.20248308 doi: medRxiv preprint trend. Additionally, we hypothesised that the "Public Transport / Transit" mobility trend uniformly influences both the above trends. We then computed the relative weights of the above activities with regards to the total activities and mapped these weights to the three mobility categories. This gave us relative weights of 0.38 for "Retail and Recreation", 0.29 for "Workplaces" and 0.33 for "Public Transport/Transit". We observe that mobility over time resembles a logistic distribution and the same is true for new confirmed cases (ܿ ௧ ), figure 1.

We observed two periods, one with a sharp decrease in mobility and one with a slight increase.

The plots of the confirmed cases follow a very similar pattern but in opposite directions. The different measures taken seem to have an effect of the slope of both lines. The fall in confirmed cases happens around 14 days after the measures have been taken and a big fall in mobility has taken place.

Based on this observation, it is reasonable to assume that there is a linear relationship between the two data series and that the available information in one period affects the decision for the next, which means that However, given that also NPIs affect mobility, we tested this hypothesis for three different periods: before advice, between advice and lockdown, and after lockdown. This hypothesis is supported by very high and significant correlation between the two variables in all three different periods (Supplementary Figure 1) .

. CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted December 16, 2020. ; https://doi.org/10.1101/2020. 12.16.20248308 doi: medRxiv preprint This observation highlights the fact that measures are not the only factors which influence mobility which in turn is related to physical distancing levels and the reproduction number of COVID-19. Behaviour should therefore be taken into account in relevant models and policy simulations.

The key variable informing NPIs is the reproduction rate, which is the fraction of the transmission rate of the epidemic (ߚ ௧ ) over the recovery rate of infected individuals (ߛ). The daily transmission rate (and hence the basic or effective reproduction rate) directly depends on the number contacts per individual, which means that due to the assumption that mobility is a proxy of daily number of contacts we can express . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted December 16, 2020. ; https://doi.org/10.1101/2020.12.16.20248308 doi: medRxiv preprint Susceptible subjects might get infected when they contact an infectious individual and if infected, they enter the exposed compartment before the infected one. Following Prem et al.

(2020) [13] , the infected individuals are split into two further groups where the first group is symptomatic and clinical ‫ܫ(‬ ௧ ) and the second asymptomatic and subclinical ‫ܫ(‬

). The first group is a fraction ߩ of the total infected and the second is

Accordingly, the evolution of the infection is given by the following set of dynamic equations [17] ), and started with 1000 people exposed at t=0.

We calibrated the constants of equation ( Using these values, our extended behavioural SEIR model was able to reproduce the dynamics of contagion in the UK (Figure 2 A, B) .

We compared the simulation results of our model with a standard SEIR (without the behavioural component) and found that the latter model predicts a number of infections both cumulative (figure 2 C) and per day, much higher than the behavioural one ( figure 2 D,E) . The difference regarding infections is several orders of magnitude, which highlights the importance of taking into account behavioural factors.

We compared the effectiveness of NPIs in our model and in the standard SEIR. As expected in the standard SEIR the cumulative number of infected individuals is lower than in the behavioural one (figure 3 A). As in the previous case, the cumulative number differs by several orders of . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted December 16, 2020. ; https://doi.org/10.1101/2020.12.16.20248308 doi: medRxiv preprint magnitude. We not that reproduction rate on the standard SEIR is only affected by NPIs ( figure   3 B) . Interestingly, we noticed that the maximum number of infected individuals at any point in time using the behavioural SEIR model is significantly and much more realistically lower than the standard SEIR ( figure 4 C, D) , where it also takes longer for the number of infected to be reduced.

We tested the impact on the total number of infected individuals and the maximum confirmed daily cases of the delay of (i) implementing the measures (ii) and lifting restrictions. This allowed us to compute the cost in terms of lockdown days in order to reach the same reproduction number. The next graph shows the dynamics of key variables compared to a hypothetical situation when the same measures had been taken 7 days earlier than the actual date of intervention.

We noticed that, while the timing of measures has an important impact on the number of . This highlights that all other factors being equal, it may be optimal to have a relatively higher reproduction rate with a lower number of infected rather than the opposite. This is due to the fact that the number of infected individuals at any point in time depends both in the reproduction rate and the number of infected in the previous period. Hence a later intervention would require a higher reduction in the reproduction number to have the same reduction in infections to an earlier one.

We tested the impact of lifting the measures earlier rather than later and also compared this to the hypothetical case of earlier timing of NPIs. As expected, the most efficient policy would be to both delay lifting physical distancing measures and implementing NPIs early (figure 5). We . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this this version posted December 16, 2020. ; https://doi.org/10.1101/2020.12.16.20248308 doi: medRxiv preprint noticed that taking the timing regarding on when the measures are lifted plays a less important role (assuming that there will be a lift) compared to the timing of imposing the measures.

The absence of a vaccine for SARS-CoV-2 has led most countries to result in NPIs in order to reduce the contagion of COVID-19 and a fast-growing literature has been focusing on estimating the effectiveness of these interventions. We argued that in order to be able to evaluate the interventions, it is necessary to explicitly take account of the behavioural change with regards to physical distancing due to both the relevant NPIs and independent individual choices. If individual behaviour is not taken into account, the levels of physical distancing without measures can be underestimated and similarly the effectiveness of measures can be overestimated. Hence, incorporating an autonomous element of physical distancing can also increase the accuracy of modelling predictions.

Using aggregate mobility data for the UK, we observed that individual mobility levels had been reducing before the measures were taken and have been increasing even before the announcement of relaxation of the measures. We tested whether information regarding confirmed cases can explain the changes in mobility within the different periods of NPIs. In order to also take into consideration, the effects of policies, we considered three distinct periods: before advice, between advice and lockdown, and after lockdown. We found high correlation in all three periods, which confirms the fact that people have been making physical distancing choices using the available information regarding the number of cases which are also assumed to be correlated to the number of deaths. We note that the number of cases reported, at the early phases of the epidemic at least, was a gross underestimate of the real cases. However, . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this this version posted December 16, 2020. ; https://doi.org/10.1101/2020.12.16.20248308 doi: medRxiv preprint the number of deaths has been used in order to infer the number of cases by imposing a somewhat arbitrary death rate. Given this as long as the number of deaths is a fraction of the number of cases the outcome of our behavioural SEIR model will not change and in addition we acknowledge that people make decisions based on imperfect information. Other studies have taken into account the structured nature of human relationships and the different transmission rates that can be realized in different places, for example care homes or hospitals can show higher transmission rates than households. We acknowledge that our model provides a higher level of abstraction that doesn't take this into account.

In order to be able to assess the effects of the different policies, we first extended the standard SEIR model to a behavioural SEIR. This model incorporates the insights stemming from the previous observations; hence it takes into account the fact that mobility is not only determined by NPIs, but also from the observed information with regards to confirmed daily cases. This incorporates a feedback effect between confirmed cases and average number of contacts between individuals, which means that the reproduction rate is (partly) endogenous.

We calibrated the behavioural SEIR model using epidemiological data from previous relevant . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted December 16, 2020. ; https://doi.org/10.1101/2020.12.16.20248308 doi: medRxiv preprint studies, values for the reproduction number based in the UK, and UK mobility data. We started our simulations with a seed of 1000 people exposed on Day 0. Genetic analysis has showed 1356 transmission lineages of COVID-19 in the UK. Our results highlight two issues. First, not taking into account the fact that individuals also react themselves over and above NPIs may lead to very misleading projections with regards to the effectiveness of measures. Second, the fact that even though the reproduction number is a relevant variable for policy purposes, it is not necessarily a measure of success of NPIs. A higher reproduction number with less active cases can be preferable to the opposite can be less challenging to the capacity of a given health system. Of course, the basic reproductive rate of the disease as defined by the biological features of the sars-cov-2 virus is still important as it is predictive of the epidemic curve in the absence of NPIs or changes in human behaviour.

. CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. Sponsor's had no role in study design, in the collection, analysis and interpretation of data; in the writing of the article; and in the decision to submit it for publication.

All data is publicly available from. [1, 12, 16] No additional data.

No clinical data from human participants has been used for this study. and is publicly available, [16] new daily cases has been downloaded form the WHO dashboard [1] and is publicly available. . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted December 16, 2020. ; https://doi.org/10.1101/2020.12.16.20248308 doi: medRxiv preprint Figure 1 .

CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted December 16, 2020. ; https://doi.org/10.1101/2020.12.16.20248308 doi: medRxiv preprint Figure 2 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted December 16, 2020. ; https://doi.org/10.1101/2020.12.16.20248308 doi: medRxiv preprint Figure 3 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted December 16, 2020. ; https://doi.org/10.1101/2020.12.16.20248308 doi: medRxiv preprint . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted December 16, 2020. ; https://doi.org/10.1101/2020.12.16.20248308 doi: medRxiv preprint Figure 5 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted December 16, 2020. ; https://doi.org/10.1101/2020.12.16.20248308 doi: medRxiv preprint

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It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprintThe copyright holder for this this version posted December 16, 2020. ; https://doi.org/10.1101/2020.12.16.20248308 doi: medRxiv preprint