- Research
- Open Access
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Analysing the link between public transport use and airborne transmission: mobility and contagion in the London underground
- Lara Goscé^{1, 2}Email author and
- Anders Johansson^{2}
- Received: 17 July 2018
- Accepted: 13 November 2018
- Published: 4 December 2018
Abstract
Background
The transmission of infectious diseases is dependent on the amount and nature of contacts between infectious and healthy individuals. Confined and crowded environments that people visit in their day-to-day life (such as town squares, business districts, transport hubs, etc) can act as hot-spots for spreading disease. In this study we explore the link between the use of public transport and the spread of airborne infections in urban environments.
Methods
We study a large number of journeys on the London Underground, which is known to be particularly crowded at certain times. We use publically available Oyster card data (the electronic ticket used for public transport in Greater London), to infer passengers’ routes on the underground network. In order to estimate the spread of a generic airborne disease in each station, we use and extend an analytical microscopic model that was initially designed to study people moving in a corridor.
Results
Comparing our results with influenza-like illnesses (ILI) data collected by Public Health England (PHE) in London boroughs, shows a correlation between the use of public transport and the spread of ILI. Specifically, we show that passengers departing from boroughs with higher ILI rates have higher number of contacts when travelling on the underground. Moreover, by comparing our results with other demographic key factors, we are able to discuss the role that the Underground plays in the spread of airborne infections in the English capital.
Conclusions
Our study suggests a link between public transport use and infectious diseases transmission and encourages further research into that area. Results could be used to inform the development of non-pharmacological interventions that can act on preventing instead of curing infections and are, potentially, more cost-effective.
Keywords
- Public transport
- Crowd modelling
- Underground
- Influenza
Introduction
Epidemic outbreaks have always been present throughout human history, affecting peoples day-to-day life. Having an improved knowledge of infectious disease spreading mechanisms and control measures is pivotal for humanity’s well-being. Furthermore, gaining a better understanding of how interactions between infective and healthy individuals lead to contagion is a crucial step in that direction. The idea behind our work arose from the necessity of creating more realistic models describing the spread of infectious diseases that could be used for policy making in order to have an impact on a population’s daily life. As an example, in the specific case of influenza, UK Department of Health, created the 2011 UK Influenza Pandemic Preparedness Strategy [1] where effective response to a pandemic are set out. The document reports that there is not enough evidence that restrictions on mass gatherings will have any significant effect on influenza virus transmission. Furthermore, from the literature and available data, there is no conclusive evidence of the individual effect of restrictions of mass gatherings to help reduce influenza transmission. As a consequence, the UK Government’s position on large public gatherings, crowded events travelling and public transport use is not only neutral in light of lack of evidences, but those types of events are even encouraged because they represent an important indicator of ’normality’ and may help maintain public morale during a pandemic [1].
When studying the spread of airborne infections on a metropolitan scale there are some environments that serve as seeds of epidemic spread, where a higher number of individuals get in contact with each other. Previous work [2] has shown that incorporating elements of pedestrian modelling [3–9]) when studying the spread of a generic airborne infection in crowded environments, can greatly improve the model’s fidelity. Combining elements of traditional compartmental models [10, 11], network models [12, 13] and wearable sensor based studies [14–16], an analytical method was recently devised [2] with the aim to be able to more accurately model small scale scenarios (i.e. pedestrian interaction). Here we apply this mathematical description to the particular case of the London Underground network by inferring a passenger transport model from data obtained from the TfL (Transport for London) [17].
Since it opened in 1863, the London Underground has become the most important transport network of the English capital and is considered the oldest rapid transit system in the world. It serves 270 stations, has 402 km of extension and carries a number of 1.265 billion annual passengers. Therefore, its stations constitute an ideal use case of crowded and confined environments and can be analysed while studying crowd dynamics and contagion mechanisms.
In the first part of our work we mathematically derive, from the TfL dataset, the time individuals take to move in a system of two stations connected with each other. Furthermore, we show how this model can be extended to a whole line of the London Underground and, from this, we evaluate the number of contacts and new infections in some selected stations. In the second part, we use real data on influenza-like-illnesses (ILI) collected by NHS from GPs in London boroughs and show the correlations between the use of the underground and new ILI infections.
Method
where πR^{2} is the area that surrounds the infective individual, according to a radius R meters which represents the maximum distance large droplets can be carried to. Consequently, in order to calculate the number of infections produced by an individual walking in a corridor, we need to calculate the average density of the whole corridor.
This means that, in order to solve the epidemiological problem of the number of new infections occurring in the stations of the network, we need to initially solve a pedestrian dynamics model allowing us to determine the time individuals take to walk inside the station at different times of the day.
In the first week of November 2009, TfL collected data from the Oyster cards (the electronic ticket used on public transport in Greater London) and made around 10% of them available to the public. When people use the underground, they tap their Oyster card once at the entrance and once again at the exit. These journeys were sampled randomly and the time stamps and Oyster card ID is reported for each entry and exit. TfL also provides a 100% sample of the total average number of entries to and exits from all the stations, every fifteen minutes. Using these data sets, we develop a method to infer the time a passengers take to walk across their starting and arrival stations. By calling A the starting station of a generic journey and B the arrival station, we can consider the total journey time as a sum of smaller trips.
The total journey time for a single passenger ΔT_{A−>B}=
the time required to walk across the starting station from the entrance to the platform \(\Delta t^{A}_{en}\) +
+ the waiting time on the platform \(\Delta t^{A}_{P} \)
+ the travel time the train takes to go from A to B, Δt_{A−>B} (for simplicity we do not consider trips that require a change of line)
Our goal is to find an estimation of the average density in the station ϱ=N/Lw (where L and w represent respectively length and width of the walked path). Since this number is clearly not constant during the day (from the station opening until its closure) because the number of people using the station N varies throughout the day, we study the average density in a time interval of 15 min and reiterate the process throughout the day. In order to do so we look at the data of the journeys in that specific time interval.
The Oyster card provide only enough data to infer ΔT_{A−>B}, while the remaining terms of Eq. (4) are unknown. To solve this problem we use data collected by a train tracking system (developed at CASA [21]) which reports the exact position of each train of the network every 3 min. By knowing the positions of all the trains in the network we are able to infer the time the train takes to move from one station to the next, and the average waiting time at the platform \(\left (\Delta t^{A}_{P} + \Delta t_{A->B}\right)\). The still analytically unsolvable equation can now be solved computationally using the method of least squares to calculate the walking time across each of the two stations.
Correlation Coefficients between the times required to traverse the station and the cumulative number of passengers entering and exiting the station in a 15-min period
Stations | Correlation coefficient | Total number of trips (n) |
---|---|---|
Bank | 0.81936 | 8092 |
Barkingside | 0.52114 | 466 |
Bethnal Green | 0.87188 | 5587 |
Bond Street | 0.83662 | 9705 |
Buckhurst Hill | 0.71433 | 949 |
Chancery Lane | 0.72835 | 5591 |
Debden | 0.72102 | 917 |
East Acton | 0.67666 | 1625 |
Gants Hill | 0.73208 | 2272 |
Greenford | 0.64114 | 1435 |
Hanger Lane | 0.84476 | 1302 |
Holborn | 0.89477 | 9414 |
Holland Park | 0.83606 | 1394 |
Lancaster Gate | 0.75767 | 1604 |
Leyton | 0.7258 | 4718 |
Leytonstone | 0.80104 | 4235 |
Liverpool Street | 0.85943 | 14723 |
Loughton | 0.52744 | 1265 |
Marble Arch | 0.90978 | 4102 |
Mile End | 0.82994 | 5501 |
Newbury Park | 0.72508 | 1655 |
North Acton | 0.69053 | 864 |
Notting Hill Gate | 0.87124 | 5058 |
Oxford Circus | 0.91423 | 16400 |
Perivale | 0.8203 | 1028 |
Queensway | 0.8781 | 2069 |
Redbridge | 0.7127 | 1026 |
Ruislip Gardens | 0.68847 | 422 |
Snaresbrook | 0.44928 | 1124 |
South Ruislip | 0.66625 | 764 |
South Woodford | 0.377 | 1643 |
St. Paul’s | 0.88929 | 5408 |
Stratford | 0.94691 | 8426 |
Tottenham Court Road | 0.90168 | 7985 |
Wanstead | 0.78013 | 944 |
White City | 0.82213 | 2953 |
Woodford | 0.80346 | 2297 |
Figure 1 highlights two important consequences arising by the use of this method: (i) the presence of peaks and (ii) the correlation between the curves.
Firstly, the model is able to capture the expected bi-modal behaviour: the morning and the afternoon peaks, meaning that, at the times when the stations are more crowded i.e. around 9 am and 6 pm when people travel to/from work it takes longer to traverse the stations. Moreover by comparing the Time Walked curve (i.e. the curve that represents the time it takes each moment of the day to cross the selected station) with the curve given by the maximum number of individuals present in the station during the day we observe a high correlation coefficient between the two. Consequently, we can say that the method captures the fact that the more crowded a station is, the longer it will take to walk through it.
Where s and i are the compartments representing susceptible and infectious individuals respectively and e is the compartment of exposed (infected but not infectious) individuals.
Influenza-like illnesses
In the second column rate per 100,000 practice population of observed number of ILI cases from October 2013 until March 2014 for each London borough (n=32) are shown
Borough | Rate of observed cases | Φ-values |
---|---|---|
Barking | 13.65 | 2.3819 |
Barnet | 10.35 | 1.0831 |
Bexley | 5 | No Underground |
Brent | 15.18 | 1.2586 |
Bromley | 5.96 | No Underground |
Camden | 12.00 | 1.2365 |
Croydon | 9.64 | No Underground |
Ealing | 7.72 | 0.9672 |
Enfield | 10.81 | 1.5157 |
Greenwich | 17.23 | 8.7555 |
Hackney | 13.16 | 1.042 |
Hammersmith and Fulham | 1.98 | 1.2096 |
Haringey | 7.73 | 3.2414 |
Harrow | 16.98 | 0.7509 |
Havering | 1.02 | 1.0846 |
Hillingdon | 9.87 | 0.2961 |
Hounslow | 1.00 | 1.3454 |
Islington | 15.37 | 2.0261 |
Kensington and Chelsea | 5.5 | 1.161 |
Kingston upon Thames | 4.9 | No Underground |
Lambeth | 12.84 | 4.3647 |
Lewisham | 11.75 | No Underground |
Merton | 8.41 | 2.1899 |
Newham | 15.67 | 4.7831 |
Redbridge | 5.54 | 1.0542 |
Richmond upon Thames | 2.3 | 1.8118 |
Southwark | 16.83 | 4.4972 |
Sutton | 8.40 | No Underground |
Tower Hamlets | 16.66 | 2.2178 |
Waltham Forest | 10.35 | 4.7722 |
Wandsworth | 11.04 | 3.3296 |
Westminster | 6.96 | 0.8579 |
In order to investigate the correlation between ILI rates in London and the contacts arising when using the underground, we define two additional parameters: (i) the total number of contacts occurring for a single passenger during their whole trip Ψ, (ii) and the total number of contacts occurring for all passengers departing from the same borough in the same time interval during the duration their trips Φ.
where 〈ρ_{i}〉 is the average density in the i-th station.
where n is the total number of trips departing from the first station, m is the total amount of trips departing from the second station and so on.
Results
We compared number of contacts calculated using our model with data collected by Public Health England (PHE) of Influenza-like illnesses (ILI) [23] and several interesting results can be highlighted.
First of all, boroughs that do no contain any underground station seem to have incidence rates lower than than average 9.73 (per 100,000). The average ILI incidence in boroughs without underground is 7.61, while it is 10.24 in boroughs with underground station. One exception is Lewisham (11.75) that, however, has a high number of railway stations (London Overground and Docklands Light Railway, DLR), here the 2011 Census [24] reported railway as the principal form of transport that residents of the borough used to travel to work. This difference, however, is not statistically significant (p-value = 0.0776).
We also notice that boroughs with higher case rates are generally more peripheral in respect to others, in particular their underground stations have a more peripheral position on the map, meaning that people who travel from there are forced not only to spend more time on the train, but also to change line one or even several times, consequently getting in contact with a higher number of individuals.
As an example we compared trips from two different boroughs: Islington and the Royal Borough of Kensington and Chelsea (RBKC). Both are very central with respect to the London map, but Islington has a case rate of 15.37 and its stations are more peripheral with respect to the underground map (the majority of the stations are served by only one line), while RBKC has a rate of 5.5 and its stations are more central and well connected and generally served by two or more lines. In order to apply our method in relation to the data, we must consider only the trips made by individuals residing in these boroughs. TfL does not provide personal data of the passengers, however not all underground users reside in London (e.g. tourists, commuters etc), moreover passengers can change position multiple times throughout the day. For this reason, we filtered our data by only considering trips with a departure time between 6 am and 10 am assuming that people leaving for work early in the morning tend to use the more convenient public transport available to them by taking the train from the station closest to their residence. After that, we evaluated all the trips leaving from the stations in these boroughs between the selected time interval, and considered the arrival stations, the lines and stations that were involved, and the total journey time. The first noticeable result is that almost all the trips departing from stations in the borough of Islington have to change line in King’s Cross St. Pancreas station which is one of the busiest and most central station of the entire underground, also connected with a major London railway terminal of the same name. Consequently, for each trip we also need to consider the time the individuals take in this station when changing from a platform to another and the number of contacts they make during the process. The majority of trips departing from RBKC are instead direct trips and do not stop at any intermediate station.
where δ_{O} is the number of contacts obtained by crossing the origin station, and δ_{D} is the number of contact resulted by crossing the destination station.
where δ_{KC} is the number of contacts made at King’s Cross.
This supports our assumption that individuals leaving from the borough with the highest incidence rate make more contacts with respect of the ones leaving from the borough with the lowest incidence rate.
Correlation coefficients between the rates of observed ILI cases and some 2015 demographic data for each borough from London Datastore [25]
Rates | Correlation coefficients | p-value |
---|---|---|
Underground related contacts | 0.44 | 0.0293 |
Population size | 0.3381 | 0.0676 |
Inner densities | 0.41 | 0.0151 |
Employment rates | -0.44 | 0.0433 |
Employment with degree | -0.08 | 1.0000 |
Benefits claimants | 0.54 | 0.0031 |
Cars per households | -0.43 | 0.0103 |
Population aged 0–15 years old | 0.13 | 0.8504 |
Population aged 65+ | -0.5782 | 0.0012 |
Discussion
The correlation between the use of public transport and the spread of infectious diseases is something that has always been assumed and generally accepted but has never been proved.
Previous studies have highlighted the importance of analysing social contacts and mixing patterns when studying infectious diseases transmitted by the respiratory or close-contact routes. In [26] data were collected by a population-based survey of mixing patterns in eight European countries through a paper-diary methodology. The definition of contact used in the study was of interactions such as a kiss or a handshake for physical contacts, while nonphysical contacts were situations such as a two-way conversation without skin-to-skin contact. In the model that we use [2], instead, we define two individuals as in contact if the local density around them is high enough that they enter in the respective infective regions that surrounds them. Another type of survey based study [35] collected data of ILI cases across UK population through Flusurvey, an internet-based open community cohort. They calculated ILI incidence week by week throughout five months, and investigated possible risk factors associated with it. One of the main conclusions of this study was that public transport does not increase the possibility of acquiring ILI. However, that study took the whole UK into account and the survey approach implied that people were able to report their symptoms at any point throughout their convalescence, moreover symptoms usually arise awhile (even days) after the contagion happens, meaning that people using public transport and people not using it have enough time to mix with each other in other environments (offices, households, etc). Consequently it is not possible to pinpoint exactly where the contagion took place, giving the macroscopic result of no connection between public transport use and incidence of new infection, while a more detailed microscopic analysis would be needed. In our work, instead of taking the whole of UK into account, we focus the attention on a local description where the underground stations are seen as confined and crowded spaces. We study the infection processes on the very first moments of the contagion, actually limiting our study to 15 min segments of intervals, knowing that the mixing patterns that arise once outside the underground network (households, offices etc) will lead to new infections that can blur the public transportation role when looking at the bigger picture. Also, studying the connection between public transport and the spread of airborne infections can highlight another issue i.e. the spatial incidence patterns over time, meaning that it could be possible to find out whether London Underground contribute to how quickly and how strongly a disease spreads to different areas of the city, areas that maybe otherwise would be reached by the disease more slowly or with lower case incidence.
The hypothesis of an association between public transport and disease transmission is not novel. Another study [36] focused on the relationship between public transport use and acquisition of acute respiratory infection (ARI). That study is closer to our work because it uses a more microscopical analysis, both in time and space. Data of ARI and control of other non respiratory conditions were collected from General Practitioners, together with data on bus or tram usage in the five days preceding illness onset (cases) or the five days before consultation (controls) and results show statistically significant association between ARI and bus or tram use. Moreover, other studies have also highlighted the importance of studying metropolitan patterns and social interactions. In [37], using travel smart card data, authors construct a time-resolved in-vehicle social encounter network on public buses in a city and draw attention to the impact of collective regularities can make on various diffusion/spreading processes. Our work, while addressing a similar question, is differentiate by the use of a novel analytical method combining individual-level pedestrian modelling and compartmental modelling. Moreover the two studies [36, 37] analyse transmission in a static setting (buses) while we address the problem in a dynamic environment of people moving inside underground stations.
The results of our study shows the existence of a correlation between the use of public transport and infectious diseases transmission. Specifically, we showed a correlation between the use of London underground and the spread of influenza-like illnesses. The model is particularly able to show this correlation in environments with high numbers of infections, capturing the fact that areas that have the highest numbers of ILI cases are also areas whose inhabitants spend more time in the underground network by changing line more frequently and getting in contact with more individuals. Correlation, however, does not prove causation, when looking at an epidemic on a large scale many contributing factors need to be taken into account. The role of social inequalities and age in the transmission of infectious diseases is well known and publicly accepted [38–41]. We compared the correlation between ILI cases and contacts originated from the use of the underground with the correlation coefficients between ILI cases and some demographic factors such as children and elderly populations, boroughs inner densities, employment rates and population on low income support (benefit claimants) and our results show similar values. While these results are not enough to quantify the role played by the use of public transport on large-scale infection transmission, they are interesting for both researchers and policy makers alike.
Limitations of this work are associated to the nature of the datasets involved. On the modelling side, Oyster card data and train tracking data were sourced in different years (2009 and 2013 respectively) and, while the underground network did not undergo major transformations during those years, results could still be affected by a level on uncertainty on the timetables. Also, PHE dataset reports numbers of ILI cases disaggregated only by borough and limited to one season, highly limiting the model’s precision in the evaluation of the correlation between infections and numbers of contacts. Moreover, knowledge of specific ILI-related data such as lengths of incubation periods or different level of infectiousness provided by the different pathogens causing ILI, would make results more precise and case specific. Further studies should focus, in particular, on sourcing individual-level ILI data in different settings so that, by combining them with already existing studies from household and schools, a clearer map of the transmission of ILI in a metropolitan environment could be drawn, this could help quantifying the role that different hot-spots play in the transmission. Empirical studies combining aero-biology and pedestrian modelling would be important in highly improving models fidelity and devising non-pharmaceutical control strategies tackling threshold densities to minimise numbers of infections and optimal ventilation in different crowded environments.
Policy makers, in particular, should address the role potentially played by public transport and crowded events and avoid encouraging the attendance of such environments during epidemics in order to maintain public morale, as specifically done by the UK Influenza Pandemic Preparedness Strategy [1].
Conclusions
In summary, we have analysed the association between the use of public transport and infectious diseases transmission by studying the London Underground network. We used real trips data to infer the level of density in each station at any time during the day and the number of contacts between passengers, and compared these results to influenza-like illnesses (ILI) rates in London boroughs. Results show a correlation between the use of the underground and ILI cases in London, specifically they show that higher numbers of ILI cases arise in those boroughs where the population spend more time in the Underground and/or incur in a higher number of contacts when travelling. On the other hand, lower numbers of ILI cases arise in those boroughs where people have a limited use of the underground and/or incur in fewer contacts. These results are in line with other environmental and demographic factors such as population stratified by ages, inner densities employment and income.
These results are informative for both scientists and policy makers alike. At the basic research stage, further studies are required to explicitly quantify the role of public transport in infectious disease transmission, and policies should be re-evaluated to take these results into account.
Declarations
Acknowledgements
We must acknowledge Dr Richard Milton at CASA (UCL) for sharing his train position data in the London Underground; Transport for London (TfL) for sharing their oyster card data; Public Health England (PHE) for their data on influenza-like illness rates in London boroughs and London Datastore for their demographic data on London population.
Funding
Not applicable.
Authors’ contributions
LG and AJ conceived, designed the study and coded the model. LG conducted the main analysis and drafted the manuscript. All authors revised the draft manuscript and approved the final version.
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
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