Transmission Transport

[Victorio Galindo]

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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.

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.

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.

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.

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.

As an example, we show here the solutions obtained when studying the Central Line (49 stations and 74km of extension). For practical reasons we show here curves for only a few of the involved stations (Fig. 1) and report in Table 1 the correlation coefficients for the other Central line stations.

Correlation coefficients for four stations on the Central line. We analysed all Central line trips arriving and departing in a given station (Liverpool Street n=14723; Notting Hill Gate n=5058; Marble Arch n=4102; Stratford n=8426). Results show a peak configuration highlighting the fact that people take more time to traverse the stations during specific times of the day. The correlation coefficient between the time necessary to walk from the entrance of the station to the platform (and viceversa) and the maximum number of individuals in the station at a specific time (data provided by TfL on the number of people entering and leaving each stations every fifteen minutes) show that these times are strictly connected to the density in the station, meaning that more crowded is an area the longer it will take to traverse it. The walking times are multiplied by 5, 10 or 20 for display purposes

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.

From the times required to walk inside each stations we can determine the transmission rate defined in Eq. 2. Finally the number of new infections that arise from the contacts happening inside each single station during the whole day can be calculated solving the simple compartmental model described in [2]

The theoretical description of the model has been presented in relation to a generic airborne human infection. In order to test the applicability of the model in a realistic context, we will now focus our attention on Influenza-like illnesses (ILI). ILI is described by the Centers for Disease Control and Prevention (CDC) as a nonspecific respiratory illness characterized by fever, fatigue, cough, and other symptoms. The majority of ILI cases is not caused by influenza viruses but by others such as rhinoviruses and respiratory syncytial virus (RSV) adenoviruses, and parainfluenza viruses. ILI infections can lead to serious complications and require hospitalization. Moreover individuals can average one to three (adults) and three to six (children) ILI yearly [22]. Table 2 reports data collected by Public Health England (PHE) [23] of the average rate per 100,000 practice population of ILI cases observed from October 2013 until March 2014 in each London borough. The data from PHE were obtained by a large surveillance system that monitors in hours general practitioners (GPs) consultations for a number of key clinical indicators. In United Kingdom individuals register with a single primary care physician who has a well defined patient population. On a daily basis this system reports and covers over 40% of the England population. Data were collected from available practices located in each London borough from October 2013 to March 2014, Table 2 reports their average value during these six months.

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.

While comparing data and results we need to keep in mind that our model is applied to the very early stages of contagion in environments considerably smaller than the usual scale (a whole city, or even a nation). To be able to perfectly compare the results from our microscopic analysis we would need individual-level data that are very difficult to acquire, thus in the comparison with PHE data (that are population-level data) we need to take into account the inferential fallacy that may occur when statistical properties observed on an aggregate level do not reflect the relations that exist on a local level. In the attempt of overcoming this problem we study the amount of contacts obtained during the whole trips when leaving from stations belonging to the same boroughs. This translate by saying that for each borough we calculate the number Φ that is given by summing for all the trips departing in each underground station of the borough between 5 am and 10 am, the total amount of contacts acquired during each whole trip. Normalised by the total number of people entering the stations of the borough (thus, consequently, the number of departures) between 5 am and 10 am (Nentry).

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.

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