1.1 Public transport demand data

The availability of suitable data is critical for city planners to tackle the current and future challenges in urban mobility. This need is amplified when there is a disruptive change in urban mobility at any scale, ranging from local short-term events such as natural disasters, social unrest, and transport supply breakdown to global long-term events such as pandemics/epidemics, economic crises and conflicts. In this context, a continuous monitoring of public transport (PT) demand changes is essential for authorities and PT operators [1,2]. In spite of the growth in the availability of higher quality data in many parts of the world, still there remain many cities that do not have access to proper data for a constant characterisation of the PT demand; or even if they have it, the available data present limitations in terms of the quality and coverage. In cities without automated data collection systems to passively record ticketing levels, traditionally, the information related to PT demand has come from datasets that have been manually collected on a small population sample. Such data, despite providing granular information, has been criticised for the lack of feasibility to be steadily applied during long periods [3]. This makes them unsuitable to analyse dynamic PT demand changes and to quantify the impacts of unexpected disruptions [4–6]. By contrast, cities that have already adopted automated fare collection (AFC) schemes have had the advantage of analysing their PT demand information from smart cards and digital transactions [7–9]. However, some limitations on the fare collection system may affect the quality of these data [10]. For example, ridership data may be lower than the actual one when ticketing are missing or incomplete, such as in the cases of ticket-free riding days or when there are special periods where fare evasion is potentially higher. Additionally, AFC systems may only cover a limited number of the PT modes present in a city (e.g. metro rails only), capturing ridership data only of those modes [11,12]. In these cases, even cities with AFC systems can benefit from secondary data sources to complement traditional ones.

1.2 Aggregated mobility indices

The increasing penetration of Information and Communication Technologies (ICT) in society has allowed several emerging datasets to be harnessed to face urban mobility challenges [13]. Call detail records (CDRs) [6], social media data [14–16], Wi-Fi and Bluetooth traces [17], and web-based ticket records [18] are some of the technologies explored in the last decade to understand the behaviour of PT passengers. Despite the effort to leverage these data to study different characteristics of PT demand, their adoption has been mainly limited to research purposes and a few case studies, as such data availability remains largely restricted [3]. Less attention, however, has been paid to the usage of data sets associated with GPS traces collected by global mobile phone apps or the level of queries in travel planner apps in the PT sector [3,19]. This situation changed in 2020, following the urgent need of health authorities, local governments, transport agencies, and the public for continuously updated and easily accessible data to deal with the COVID-19 pandemic.

Aggregated mobility indices (AMIs) based on ICT were globally provided by tech companies during the COVID-19 pandemic to describe human mobility patterns in cities. AMIs were based on data collected from the regular use of mobile devices associated with GPS and apps, technologies that were already part of tech companies’ products and services [20]. The information was aggregated to describe human mobility behaviour within cities, offering a near-complete coverage of the urban grid and a large proportion of the population. AMIs were used to analyse mobility trends and scenarios, and assess the effectiveness of mobility restrictions on human mobility [5,21–25]. AMIs were also employed in studying COVID-19 transmission [26], pandemic indicators [26,27], air quality [28,29] and economic recovery [30], among other topics. Big Tech companies such as Google and Apple shared reports on the aggregated mobility changes of the population at a city or regional scale between 2020 and 2022 [31,32]. Other companies, such as Moovit and Citymapper, which run travel planner apps, also offered similar mobility indices [33,34].

Among the AMIs proposed, Google COVID-19 Community Mobility Reports (GCMR) and Apple Mobility Trend Reports (AMTR) were the most popular. GCMR were based on the variation of human movements across different categories of locations (residential, workplace and public transport stations, among others) [35]. To measure the mobility changes related to PT, GCMR considered the access frequencies and the time spent on PT hubs (bus stops, train stations, etc.). The relative change was estimated by comparing a mobility level with a pre-pandemic baseline value. Some uses of the GCMR’s PT index were the characterisation of the use of PT, the clustering of cities with similar PT demand change levels, and the assessment of the effectiveness of mobility restrictions [4,12,21,36–38]. On the other hand, AMTR reported indices estimated based on navigation data from the Apple Maps app service to describe its users’ mobility trends [32]. AMTR showed daily relative changes for three transport modes (PT, walking and driving) by estimating the quotient between the volume of direction requests for a specific day and pre-pandemic baseline [20]. The characterisation of the change in mobility was one of the main uses of this data set [4,21,39–41].

1.3 Ridership data versus AMIs

Despite the widespread use of the AMIs provided by tech companies during the last three years, it is surprising that limited evidence of the reliability of these indices to represent actual PT demand shifts is available. As the importance of mobility data availability transcends the COVID-19 pandemic, a proper assessment of the potential of AMIs in PT is desirable for wider applications. So far, comparisons between AMIs that offered proxies for PT and ridership data have been provided tangentially by a few studies that analysed both data sources when characterising COVID-19’s impact on PT demand. These studies preliminarily reported that AMI captured the generalised drop in ridership during the pandemic outbreak and that after it, they overestimated PT demand recovery [34,42]. For instance, using ridership data, a study conducted in Sweden [42] reported a reduction in PT demand of 40% in Skåne, 50% for Västra Götaland and 60% for Stockholm at the end of June 2020. By contrast, using the PT index of GCMR, the same study observed only a 0%, 10%, and 20% reduction in ridership, respectively. When they explored the PT index of AMTR, they obtained a reduction of around 20% with no noticeable difference between those areas. A smaller difference was observed in New York, where a 50% ridership decrease was observed using the PT index of AMTR when a 70% reduction was reported by the subway transactions [11]. In a study conducted on the Community of Madrid also for 2020, the authors contrasted smart card records with the Moovit mobility index. They found that during the recovery stage, the Moovit index reported a drop of only 5% compared to a reduction of 50% recorded for the ridership data [34]. Despite this evidence, several limitations in the existing studies lead to inconclusive findings about the level of accuracy of AMIs in terms of replicating PT ridership changes and their potential for wide-spread use in PT planning and operational decisions:

1. Early comparisons overlooked differences in the methodological approaches used to estimate AMIs. Therefore, the benchmarking required for properly comparing the datasets is yet to be conducted.
2. As the primary goal of the above-mentioned studies was to describe PT demand changes and not to assess the similarity between ridership data and AMIs, they did not conduct a formal quantitative comparison, limiting the current evidence to point-temporal comparisons and visual inspections of the trends only. In addition, as these early insights are based on data from the first half of 2020 and a few isolated contexts, there is a significant gap in the literature in studying a more comprehensive period and a wider sample of cases.
3. To the best of our knowledge, attempts to leverage the complementary role of AMIs on traditional ridership data have yet to be done (e.g., fill in temporal gaps in the data, identify supplementary information, etc.).

To address these gaps, this study aims to conduct a comprehensive similarity evaluation between the changes reported by AMIs for PT demand and ridership data. Monthly ridership data from 12 cities worldwide from eight countries and daily ridership for three case studies (London, New York and Santiago de Chile) were used for the analysis. Similarity metrics assessed the agreement between AMIs and ridership data for the period 2020–2022. Seasonal ARIMAX models were also employed to test the capacity of AMIs to predict PT demand changes in periods where ridership data did not record the actual demand. The results of this study provide a more comprehensive understanding of similarities and differences between the two data sources and reveal the potential role of AMIs in PT demand characterization, particularly in developing countries.

The remainder of this paper is structured as follows. The methodology of this study is provided in Section 2, including a description of the data and a definition of the metrics used to measure the degree of similarity between ridership data and AMIs. Section 3 shows the results of the similarity comparison and Section 4 presents the complementarity analysis between AMIs and ridership data. Finally, the implications of the findings and future perspectives are discussed in Section 5.

2.1 Data

Two AMIs that offered proxies for PT were retrieved to be tested in their alignment with ridership changes. We selected Google COVID-19 Community Mobility Reports (GCMR) and Apple Mobility Trends (AMTR) as they offered global coverage and the most prolonged availability [31,32]. Additionally, they present proxies for PT use based on different ICT sources: GCMR used GPS traces from smartphones, and AMTR employed the queries for PT made in the Maps application of Apple devices (a further description of these indices is provided in Section 1.2). In this work, we will use the term Human Mobility Index (HMI) to refer to the particular index in the GCMR that measured the changes in human mobility in PT hubs (train stations, bus stops, etc.). Analogously, we will use the term Apple Query Index (QI) to refer to the category of AMTR that compared the level of queries for PT directions in Apple Maps. Both indices were updated daily from 2020 to 2022. Specifically, HMI was provided from 15 February 2020 to 15 October 2022 and QI from 13 January 2020 to 12 April 2022 (AMTR data for 11–12 May 2020, 12 March 2021 and 21 March 2022 were unavailable). On the other hand, ridership data came from validations made by smart cards and paper or digital tickets and were directly retrieved from the official portals of several PT operators. The inclusion criteria for selecting an urban area as a case study considered the availability of ridership data and AMIs. A total of 12 different case studies were selected (considering a monthly temporal resolution of ridership), aiming to include different contexts and increase the generalization of the similarity assessment. In only three of them, daily ridership data were publicly available (London, New York and Santiago de Chile). Both, monthly and daily ridership data were used in the similarity analysis (See S1 Table). Table 1 specifies the case studies included in the analysis, indicating the availability of AMIs as well as the temporal and spatial resolution of the retrieved ridership data. This work employed publicly available data, whose use complied with the terms and conditions for each source. Further details of the terms and conditions can be found directly in the web pages of each source using the links provided in the Supporting files (S1 Table).

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Table 1. Case studies for the comparison between AMIs and ridership data.

https://doi.org/10.1371/journal.pone.0296686.t001

2.2 Establishing a common definition

To generate comparable datasets, a common basis for estimating mobility changes was adopted. This common basis was required due to differences in how AMIs were reported and the absolute nature of the ridership data (i.e. the total number of transactions), aspects that were ignored in early comparisons. The GCMR and AMTR reported daily relative changes by estimating the quotient between the mobility volume for a specific day and a baseline mobility volume defined for the pre-pandemic. The proportion obtained was reported as a percentage, and a positive value indicated the percentage of increase with respect to the baseline, while a negative one specified the degree of reduction. However, the baseline definition adopted by each index was different. As the QI employed as a baseline the number of queries of only one day, this index was more susceptible to high variability due to the lack of inclusion of weekly mobility cycles. In the case of ridership data, a normalisation of their values respecting a baseline was also required to obtain a relative scale. A review of the criteria employed in the literature for estimating relative changes with aggregate PT demand supported the baseline definition adopted by the HMI [34,43], and for this reason, it was employed as the consistent basis in the current paper. The definition includes the choice of a pre-COVID-19 period, the recognition of demand variability within the week and a way to deal with potential outliers. As no AMIs were available before 2020, using data from 2019 to describe the pre-pandemic period was not possible. Both ridership data and the QI were adapted according to the HMI’s baseline definition. We present the details of the baseline definitions adopted for the case studies where daily ridership was available in Table 2. Table 2 also explores the consistency of daily values for ridership and the QI in the baseline period. Coefficients of variation smaller than 6.0% were observed, revealing high stability in the mobility trends of the same days of the week for the period that characterised the pre-pandemic. It was interesting to observe also for this period that the QI depicted the highest demand for PT information on Fridays and Saturdays, contrasting with the typical daily variability of ridership data (See S1 Fig).

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Table 2. Details of the common baseline adopted to estimate relative changes in ridership data and the QI.

https://doi.org/10.1371/journal.pone.0296686.t002

The expressions used to apply the common basis on ridership data and the QI are presented in Eqs 1 and 2. We call these new indices relative ridership change index (RRC) and Apple query modified Index (QMI). The RRC at a time t (RRC_t) was defined as follows: (1) Where r_t is the ridership on day t (t = 1, 2, …, T) and R_f(t) is the baseline ridership for each day of week f, whose value in Eq 1 depends on the day of the week corresponding to t. If both r_t and its corresponding R_f(t) were the same, the quotient is one and the RRC_t is equal to zero (i.e. 0% change). The RRC takes a negative value if the ridership in the time t is smaller than the one existing in the baseline period for the corresponding day of the week. For instance, if the ridership were half compared with the baseline value, the index would be equal to -50 (%). The same interpretation apply for the HMI. In the case of New York, daily ridership was not available for January. Therefore, we use the reported average value of ridership for weekdays, Saturdays and Sundays during January 2020 as baseline values. To estimate RRC for the case studies where only monthly ridership was available, we first estimated the average daily ridership for each month, dividing monthly ridership by the number of days of each month. Then, the RRC was estimated analogously, employing the average daily ridership of January 2020 as a baseline value.

In the case of the QI, its original values were reported as percentage changes relative to one particular day. Apple provided these values on a base of 100, assigning a value of zero to the QI of 13 January 2020. Then a value of 5.0 would indicate that for a particular day, the number of queries was five percent higher than the base day. The adoption of the common baseline for estimating relative changes for this index was addressed by proposing the Apple’s query modified index (QMI): (2) Where QI_t is the Apple’s query index on day t (t = 1, 2, …, T) and QIB_f(t) is the Apple’s query index baseline for each day of the week f, whose value in Eq 2 depends on the day of the week corresponding to t. Each QIB was estimated as the median QI value for the same day over the three weeks between 13 January and 2 February 2020 (as there were no earlier values). In this way, the QMI overcomes the original limitation of the QI, comparing query levels of the same days of the week and controlling for outliers if they were present. The QMI shares the same interpretation with HMI and RRC. Monthly QMI and HMI were obtained by averaging their daily values for each month.

2.3 Similarity assessment

The degree of similarity between the values reported by AMIs (HMI and QMI) and RRC was assessed by applying metrics under a time series approach. For the monthly analysis, we included the mean Euclidean distance (MED), the cosine distance (COS) and a trend similarity index (TSI). The Dynamic Time Warping distance (DTW) and the Granger Causality test were included for the daily similarity analysis where a higher granularity in the data was available. The MED is recommended when a straightforward interpretation of the differences is required. In our case, as the time series values are all relative changes (%), the MED interpretation is the average distance in percentage points between the relative change reported by the AMIs (HMI or QMI) and RRC. The COS is a similarity measurement between two vectors defined in an inner product space [44]. Their values are always between -1 and 1, where 1 means perfect alignment and -1 indicates the opposite. DTW is an alignment-based metric that estimates the Euclidean distance between two time series that may not be aligned [44]. We included DTW for the daily analysis to deal with potential shifts in the times series, particularly present in the QMI. The Granger Causality test determined whether AMIs could be used to forecast the RRC values [45]. This statistical hypothesis test uses Student’s statistic and F-statistic tests to determine whether values of a certain variable provide statistically significant information about the values of Y. The trend similarity index (TSI) was estimated as the proportion of slopes with the same sign for the same pair of consecutive months/days between the RRC and AMIs. The sign of the slopes for two consecutive times was obtained by observing the direction of the change between the values of each index. The TSI between RRC and an AMI (HMI or QMI) was defined as: (3) (4) Where Δ indicate the difference between two consecutives values for the respective index, and T is the length of the time series. TSI metric ranges between 0 and 1, where the value one means that the AMI replicated exactly the same direction of change of the RRC and zero the case of a complete disagreement.

2.4 Complementary role of AMIs

We also explore the complementary role of AMIs in contexts where ridership data did not capture the actual PT demand and on atypical days where mobility demand was extraordinarily high. Hence, the next situations helped illustrate the role that AMIs may play in complementing ridership data:

1. Free bus travel period in London during the pandemic outbreak: From 20 April to 30 May 2020, Transport for London introduced middle/rear-door-only boarding in bus services to take care of drivers. AMIs were used here to reveal an approximation of the actual PT demand in this period where ridership was under-reported.
2. Partial ridership data in New York MTA: No bus ridership data collected directly from a smart card or ticketing validation was available for the New York MTA between 1 March and 30 September 2020. Using AMIs, an approximation of the actual RRC in this period was estimated.
3. High mobility demand day for Santiago: The day of the national referendum in Chile (Sunday, 4 September 2022) was marked by an extraordinarily high mobility, resulting in the highest recorded RRC for Santiago in the study period. We assessed the discrepancies between the predicted RRC (based on the AMIs) and the recorded RRC.

Autoregressive Integrated Moving Average (ARIMA) models were employed to calibrate the relationship between the recorded RRC and the AMIs. For this, we selected the AMI that exhibited the highest similarity with RRC, while the calibration was made on periods with the most stable conditions available. ARIMA models are particularly efficient and appropriate when successive observations show serial dependence (e.g. in this case, daily observations), and therefore, the assumption of independent errors typically made for cross-section regression data is violated. At the same time, this modelling approach allows testing whether the AMI contribution to explain RRC is statistically significant. As a weekly periodicity was also found in the descriptive analysis (see S2 Fig), an appropriate model specification may consider both, daily and weekly autocorrelation. To consider both correlations, a multiplicative seasonal ARIMA model is specified, where one component (p, d, q) captures the daily correlation, and a second component (P, D, Q) explains the weekly correlation in the data. If s is the seasonal period of the time series (considering weekly seasonality s = 7), then the seasonal ARIMAX (p, d, q)×(P, D, Q)[s] [46] can be written as follow: (5) where y_t is the value of the RRC time series for the time t. ε_t is the white noise process (i.e. random error, i.i.d. Gaussian (0, )) and L is the backshift or Lag operator, defined as Ly_t = y_t−1. d represents the differences that can be applied on the dependent variable to obtain a stationary time series for the non-seasonal model. Φ_p(L) is the polynomial of order p that contains the marginal contribution of the auto-regressive (AR) component and Θ_q(L) the polynomial of order q of the moving average (MA). is the operator of the seasonal AR component with order P, D is the seasonal differences number and is the operator for the seasonal MA with order Q. Note that we have added in the last term of Eq 5 the AMI, which is an exogenous variable in the modelling with coefficient ω.

3.1 Monthly analysis

A monthly analysis of 12 cities worldwide from eight countries showed that HMI and QMI were capable of replicating the RRC with different degrees of accuracy. Fig 2 presents the monthly variability of each index for the entire study period per case study, while Table 3 presents the results for the similarity metrics. Overall, AMIs correctly mimicked the main direction of changes depicted by RRC. In all the cases considered, AMIs properly replicated the drop in PT demand during the pandemic outbreak. However, in most cases, AMIs reported higher PT demand recoveries than the RRC. The average MED for the HMI and QMI were 11.9 and 11.6 for 2020 and 14.4 and 26.6 percentage points for the entire period, respectively. Cities like London and Sydney exhibited the greatest match between HMI and RRC, with small MED obtained (5.1 and 4.0). However, common MED were between 10 and 20 percentage points for most studied cases. Regarding the QMI, this index exhibited a similar adjustment to HMI until April 2021. After this date, QMI showed a general increase until August 2021, when the index stabilised around 60 percentage points above RRC values. The Similarity Trend Index (STI) ranged from 0.71 to 0.94 for the HMI and 0.73 to 0.92 for the QMI, revealing a high capability to replicate the direction of change of the monthly ridership trends by the AMIs. The cosine distance values supported these results showing magnitudes that indicate high similarity. Case studies where only partial ridership information was retrieved showed higher differences compared with the general trends. For instance, the greatest difference between HMI and RRC was observed in Bogota. This may be explained as ridership data for Bogota only describes the BRT system’s demand and does not consider the local bus system. Moreover, contrary to the remaining case studies, AMIs in Taipei and Hong Kong reported lower PT demand recovery than the RRC. This difference may be explained by considering that only metro ridership was available for these two cities.

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Fig 2. Average monthly changes in HMI (orange), QMI (green), and RRC (blue).

Centre of the graphic indicates -100% change, central grid circumference 0% change and external grid circumference +60% change (all compared with baseline values). Data from February 2020 to October 2022 (for some case studies, available ridership data end in July 2022).

https://doi.org/10.1371/journal.pone.0296686.g002

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Table 3. Monthly similarity metrics between AMIs and RRC.

https://doi.org/10.1371/journal.pone.0296686.t003

3.2 Daily analysis

The daily analysis compared HMI and QMI with RRC for the cities of London, New York and Santiago. Fig 3 provides a graphical illustration of the aggregate PT demand shifts depicted by each index. The HMI was found to match surprisingly well with the daily RRC time series. At the same time, the QMI displayed a reasonable fit in terms of the magnitude of the PT demand recovery until the first half of 2021. For that period, the main trends of peaks and troughs of the RRC time series were also depicted appropriately by HMI and QMI, including short sharp reductions during holidays. A particular concurrence of the values of all indices was observed during the periods where the stricter mobility restrictions were in place (pandemic outbreak and from November 2020 to February 2021).

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Fig 3. Daily variation of PT mobility indices.

HMI, QMI and RRC for the case studies of London, New York and Santiago.

https://doi.org/10.1371/journal.pone.0296686.g003

To identify changes in the pattern of the dissimilarity between the AMIs and RRC, Fig 3 also presents the differences between them for each day. A positive distance indicates that the AMIs observed a lower relative drop or a higher relative increase than the RRC. The difference between HMI and the RRC showed relatively constant values, whilst the difference between QMI and the RRC exhibited greater variability. In general, mostly positive differences were observed, except for London, where the HMI generated negative differences from May 2021 onwards. This situation coincides with changes in the fare scheme for children, which involved removing free travel for some ages. The highest dissimilarities in the London case between HMI and RRC were observed from April to May 2020, when mandatory payments in London’s buses were suspended. In the case of New York, a change in the trend of the differences was observed during the first half of 2020, where RRC was represented only by the subway ridership. In the case of Santiago, the most remarkable observed differences were associated with sharp peaks in the HMI during special events (e.g. national elections and referenda). For the QMI, the highest differences with the RRC were observed during the first recovery period (June to November 2020) and during the second recovery (April 2021 onwards, where QMI was considerably higher). A ratio of increase in the number of PT queries greater than the recovery in the actual ridership during the first half of 2021, when many restrictions were eased, would explain these discrepancies. This interpretation is supported by the results of Sydney (see Fig 2), where its QMI experienced a similar increase when a similar ease of mobility restrictions started in that city at the end of 2021.

Similarity metrics presented in Table 4 support the descriptive analysis based on Fig 3. Considering the entire period, the MED for the HMI were 6.2, 9.1 and 18.2 for London, New York and Santiago, respectively. In the same order, standard deviation values of 5.8, 4.5 and 5.7 were calculated, indicating consistency among the case studies in terms of the differences between the HMI and the RRC. For each case study, the MED of HMI was seen to be relatively constant across the three years, showing great stability in its capabilities of replicating the changes reported by ridership data. In the case of the QMI, an overall MED of 35 percentage points was estimated for London and New York. Contrasting with the HMI results, the QMI showed an increasing difference along the time series with the RRC. Moreover, the standard deviation of the MED of QMI ranged from 26 to 28 percentage points, considerably higher than the one estimated for HMI. The analysis based on the DTW distance offered a similar interpretation for the AMIs. The Similarity Trend Index (STI) showed that the HMI replicated correctly between 75% and 85% of the RRC trend change directions; in the case of the QMI, the STI dropped to values from 54% to 74%. This may be explained considering that RRC and HMI depicted higher PT demand recovery on weekends, while QMI reported greater values on Fridays and Saturdays (see S2 Fig). The cosine distance indicated that QMI only presented a high similarity with RRC during 2020 and the Granger Causality Test indicated that both HMI and QMI could be used to predict RRC.

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Table 4. Similarity metrics between AMIs and RRC, daily analysis.

https://doi.org/10.1371/journal.pone.0296686.t004

4.1 London case study

The fitted and forecasted RRC for the London case study are shown in Fig 4A and 4B. Modelling results suggest a substantial under-reporting in ridership due to the free-bus policy enacted from 20 April to 24 May 2022 (see Fig 4B). The difference between recorded and predicted RRC was at least 20 percentage points when the free-bus trip policy started on 20 April 2020. The predicted RRC (using forward and backward forecasting) coincided with the under-reporting magnitude, showing only that the forward forecasting generate a slightly more conservative prediction of the RRC. Predicted RRC suggested that the actual PT demand started to recover at the end of April 2020, not at the end of May, as the recorded RRC shows. Thereby, the dissimilarity between recorded and predicted RRC increased as PT demand started a slow and gradual recovery that ridership data did not take into account. The results also revealed that even when the free-bus policy finished on 24 May, the under-reporting in ridership continued for several months, gradually decreasing. In fact, according to Fig 4B, it took at least two months after the end of the free bus policy to observe the unification between the recorded and predicted RRC. This finding revealed a gradual adaptation process of PT users to return to normal payment behaviour after experiencing a free bus ride policy, which ridership data was unable to observe.

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Fig 4. Predicted RRC using calibrated HMI for London.

(A) Results for the fitting and validation period, (B) Forecasting for the research period (95% confidence intervals).

https://doi.org/10.1371/journal.pone.0296686.g004

4.2 New York case study

Graphical results for the New York case study are provided in Fig 5A and 5B. Here, using HMI, it was possible to obtain an approximation of the actual ridership change in the city during the research period (see Fig 5B). To understand these results, two facts may be recalled from the New York data description: a) recorded RRC from 1 March to 30 September 2020 are based only on subway validations, and b) data from 1 October onward contain both bus and subway ridership data. Thereby, as the calibration between RRC-HMI is made when the complete data are available, the predicted RRC illustrates an approximation of the actual ridership in the New York MTA, as both bus and subway ridership would have been available. The results suggest that the actual changes in ridership in the system were lower in magnitude than the only-subway changes. Therefore, bus ridership should have experienced lower changes than the subway during the research period. In fact, the estimation showed that bus ridership was, on average, about 20 percentage points above the recorded relative subway changes for the period. It is interesting to notice that, as the predicted RRC is depicted below the recorded RRC on the first weeks of March 2020, the backward forecasting of RRC should be seen as a conservative approximation of the true RRC in terms of actual ridership recovery.

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Fig 5. Predicted RRC using calibrated HMI for New York.

(A) Results for the fitting and validation period, (B) Forecasting for the research period (95% confidence intervals).

https://doi.org/10.1371/journal.pone.0296686.g005

4.3 Santiago case study

Fitted and forecasted RRC for the Santiago case study are presented in Fig 6A, while Fig 6B zooms in on a fraction of the validation period. The results of the RRC prediction for the Chilean national referendum on 4 September 2022 showed that the HMI overestimated the recorded RRC (30.2% vs. 17.2%, see Fig 6B). This difference was much higher than any other prediction error observed in the validation period, suggesting that the reason for that difference was an exceptional overestimation in the mobility on PT hubs registered by the HMI. Several elements that may have influenced the overestimation in the predicted RRC are hypothesised, related mainly to the nature of the HMI. For instance, a high HMI value may be associated with an increment in the time spent in PT stations due to higher waiting times of PT users caused by either a high demand or a limited PT supply. In fact, on 19 December 2021 (also an election day), Santiago’s PT supply was severely criticised for the lack of bus services, low frequencies and unusually long waiting times. Interestingly, that day Santiago’s HMI exhibited its highest value (57.1%) and highest difference with the RRC. An additional feasible cause of the HMI overestimation is linked to the exceptional nature of a national referendum, which involved millions of people travelling to their assigned locations. This generalised and exceptional number of people on the street may have affected the MI, for instance, by increasing pedestrian activity near PT hubs. In consequence, even when HMI successfully predicted RRC on regular days (including public holidays), it may be susceptible to registering higher mobility levels than the actual ridership on days with exceptional mobility.

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Fig 6. Predicted RRC using calibrated HMI for Santiago.

(A) Results for the fitting and validation period, (B) Forecasting for the research period (95% confidence intervals).

https://doi.org/10.1371/journal.pone.0296686.g006