The impact of COVID-19 pandemic on the fundamental urban mobility theories using transit data from Singapore

Mepparambath, Rakhi Manohar; Huynh, Hoai Nguyen; Oon, Jeremy; Song, Jie; Zhu, Rui; Feng, Ling

doi:10.1016/j.trip.2023.100883

Urban systems · Transportation Research Interdisciplinary Perspectives 2023

The impact of COVID-19 on the fundamental urban mobility theories, using transit data from Singapore

Rakhi Manohar Mepparambath, Hoai Nguyen Huynh, Jeremy Oon, Jie Song, Rui Zhu, Ling Feng

Institute of High Performance Computing, A*STAR Singapore · Department of Physics, National University of Singapore

COVID-19 changed how much people in Singapore travel by bus and train. Did it also change the laws that say where they travel? We fitted the three best-known mobility laws to transit flows before, during and after the pandemic. All three still hold, but their ranking and their parameters moved.

Paper (open access) fengling.eth

The claim

The mobility laws survived the pandemic; their parameters did not.

The visitation law predicts flows best in all three stages. The gravity model improved by 6–18 % during the pandemic and 9–15 % in the endemic stage, while the parameter-free radiation model barely changed. Floor area predicts flows better than resident population in the gravity and radiation models; for the visitation law, population is better.

0 · Context

Laws that held in every city before 2020 had not been tested after it

Human mobility has a few laws that describe flows between places with remarkably little information: the sizes of the places and the distance between them. They were found to hold in cities around the world, which is why they are used to plan land use and transport. All of them were derived and tested on data from before the pandemic.

COVID-19 changed daily life twice over: in the short term through lockdowns and movement restrictions, and in the long term through hybrid work. Many studies documented the drop in travel during the pandemic; very few asked whether the laws of mobility changed with it. We re-examined three of them, the gravity model, the radiation model and the visitation law, on Singapore’s public transport at three stages: pre-pandemic, pandemic and endemic.

Condensed from Table 1 of our paper. We compare January 2019 (pre-pandemic), June 2020 (pandemic: the circuit breaker had the strictest rules, but detailed origin–destination data are not available for it, so we use the next most restricted month) and April 2022 (endemic).
Period	Phase in Singapore	Social gatherings	Workplaces
Jan 2020	First confirmed case	no limit	no limit
Apr–May 2020	“Circuit breaker”	not allowed	all work from home
Jun 2020	Phase 1 reopening	not allowed	all work from home
Jun–Dec 2020	Phase 2 reopening	up to 5	up to 50 % may return
Jan–May 2021	Phase 3 reopening	up to 8	up to 70 % may return
May–Nov 2021	Phase 2, heightened alert, stabilization	2 to 5	50 % to all from home
Nov 2021–Apr 2022	Transition phase	5 to 10	all from home to 75 % may return
Apr 2022 on	COVID-19 resilient nation	no limit	all may return

1 · Data

Every bus and train trip, aggregated to 55 planning areas

Map of Singapore's planning areas coloured by land-use group: commercial in the centre, residential across most of the island, industrial in the west, mixed, reserved and other areas. — **Fig. 1.** The 55 planning areas, grouped by land-use composition into commercial, residential, residential/industrial mixed, industrial, reserved and other.

Public transport carries most trips in Singapore: 67 % of peak-hour trips use the train (MRT and LRT) or the bus. The Land Transport Authority publishes the number of trips between every pair of stops, hour by hour. We aggregate these origin–destination (O-D) flows to the 55 planning areas of the Urban Redevelopment Authority’s Master Plan 2019.

Distances are measured on the transit network, not as the crow flies: the distance between two areas is the flow-weighted average of the shortest transit distances between all stop pairs observed between them. Using the distance between area centroids instead changes the results only negligibly.

Each area has two candidate “masses”: its resident population (2020 census; 13 areas have no residents) and its gross floor area (GFA), the maximum floor area that may be built there, summed from the Master Plan’s land parcels. Population counts where people live; floor area also measures where they work, shop and study.

2 · What changed

Fewer trips, the same distances, and a shift towards green spaces

Transit ridership fell most during the first wave, April to June 2020, and dipped again with the second wave in May–June 2021. Each later wave caused a smaller dip, the sign that Singapore had entered the endemic stage. Ridership has not returned to its pre-pandemic level, possibly because many companies kept hybrid work.

4.25 + 3.68 M

Jan 2019, pre-pandemic: average daily bus + train trips

2.13 + 1.35 M

Jun 2020, pandemic

3.44 + 2.78 M

Apr 2022, endemic

Line chart from January 2019 to January 2023 of average daily bus trips and train trips in millions, with daily COVID-19 cases. Both trip curves drop sharply in April 2020 and recover only partly; the three study months are marked. — **Fig. 2.** Average daily transit trips, Jan 2019 – Jan 2023, with daily COVID-19 cases; the three study months are marked in red. Tap to enlarge.

Box plots of trip distance for bus and train in the three periods; the boxes are nearly identical across periods, train trips being longer than bus trips. — **Fig. 3.** Trip distances by bus and train in the three stages.

The length of trips did not change: the distributions of bus and train trip distances are nearly the same in all three stages (Fig. 3). What changed is where trips start and end. Most areas lost trips in both the pandemic and the endemic stage, the most in areas with high residential and commercial land use (Fig. 4, blue). A few areas gained trips (orange); these have a relatively large share of parks and green spaces.

This points to a long-term change in how many trips each type of land use generates, which flexible work may partly drive.

Four maps of Singapore coloured on a symmetric log scale from dark blue (large decrease) to red (increase): changes in trip origins and destinations from pre-pandemic to pandemic and from pre-pandemic to endemic. Most areas are blue; a few are orange. — **Fig. 4.** Change in trip origins (a, c) and destinations (b, d) from pre-pandemic to pandemic (top) and to endemic (bottom). Blue: fewer trips; orange/red: more. Grey: excluded. Tap to enlarge.

3 · Three laws

Three ways to predict a flow from masses and distance

Each law predicts the number of trips $T_{ij}$ from area $i$ to area $j$ , separated by distance $r_{ij}$ . We use either population or floor area as the mass $m_i$ of the origin and $n_j$ of the destination.

Gravity model

Like Newton’s law

T_{ij}=G\,\frac{m_i^{\alpha}\,n_j^{\beta}}{r_{ij}^{\gamma}}

Flow grows with both masses and falls with distance. We fit all four parameters $G,\alpha,\beta,\gamma$ (the “Type I” form) by linear regression in log–log space.

Radiation model

Intervening opportunities

T_{ij}=T_i\,\frac{m_i\,n_j}{(m_i+s_{ij})(m_i+n_j+s_{ij})}

Simini and co-workers’ parameter-free law: what matters is $s_{ij}$ , the mass within a circle of radius $r_{ij}$ around $i$ (excluding $i$ and $j$ ). $T_i$ is the total outflow of $i$ .

Visitation law

Distance × frequency

T_{ij}=\frac{\mu_j A_i+\mu_i A_j}{r_{ij}^{2}\,\ln(f_{\max}/f_{\min})}

Schläpfer and co-workers found that visitors to a place fall as $(rf)^{-2}$ with distance $r$ and visit frequency $f$ . For aggregate flows, $\mu$ is set by population density and $A$ is the area; no parameter is fitted.

For the visitation law, $\mu_j\approx\rho_{\text{pop}}(j)\,r_j^2\,f_{\text{home}}$ , with $\rho_{\text{pop}}$ the population density, $r_j$ the distance to the boundary of $j$ and $f_{\text{home}}=1/\text{day}$ , assuming people return home daily. Since our flows are daily, both frequency limits are one per day. To compare models, we use the Sørensen–Dice similarity index (SSI) between predicted and observed flows,

\mathrm{SSI}=\frac{2\sum_{i,j}\min\!\left(T^{\text{pred}}_{ij},T^{\text{obs}}_{ij}\right)}{\sum_{i,j}T^{\text{pred}}_{ij}+\sum_{i,j}T^{\text{obs}}_{ij}} ,

(6)

which is 0 for no agreement and 1 for a perfect match.

4 · Results

All three laws still hold, and the visitation law is still the best

Every law reproduces the observed flows in every stage. The ranking, however, moved: before the pandemic the gravity and radiation models performed about equally; since then the gravity model has pulled ahead, while the radiation model stayed where it was. The visitation law with population is best throughout.

Model comparison · Table 3 of our paper

Sørensen–Dice similarity index, higher is better

mass variable

—

Bars from 0.4 to 0.7. With population, the gravity model gains 18 % in the pandemic and 15 % in the endemic stage; with floor area, 6 % and 9 %. Switching to floor area helps the gravity and radiation models but hurts the visitation law.

Six log-log scatter plots of predicted against observed flows for the gravity model: top row with population (teal), bottom row with floor area (orange), for pre-pandemic, pandemic and endemic stages, with the SSI value in each panel and the diagonal line of perfect prediction. — **Fig. 5.** Gravity model: predicted vs. observed flows between planning areas, with population (a–c) and gross floor area (d–f), pre-pandemic, pandemic and endemic. The diagonal is a perfect prediction. Tap to enlarge.

Radiation model. Its performance hardly changed (SSI 0.501–0.518). Floor area works as well as or slightly better than population, although the model was proposed for population. Its largest errors are under-predicted flows from residential to industrial areas: industrial areas have almost no residents and comparatively little floor area, so the model sees little to attract trips there.

Visitation law. It stayed best, with a slight drop for the population version during and after the pandemic. Floor area makes it worse in all three stages. A likely reason is that the law’s aggregate form was derived from population density and from people returning home daily; neither assumption holds for non-residential land. It over-predicts flows between industrial areas and dense areas, and under-predicts flows between dense residential areas. For both the radiation model and the visitation law, these errors suggest that adding the land-use type could improve predictions; the gravity model suffers less because it fits separate exponents for origin and destination.

Six log-log scatter plots of predicted against observed flows for the visitation law, population in the top row and floor area in the bottom row, for the three stages, with SSI values. — **Fig. 7.** Visitation law, same layout as Fig. 5. (Fig. 6 of the paper shows the radiation model.) Tap to enlarge.

5 · Parameters

Distance matters more since the pandemic, and the masses matter less

The fitted gravity parameters show how mobility changed, even though the law itself survived.

Table 2 of our paper: gravity-model parameters.
Stage	$\alpha$ (origin)	$\beta$ (destination)	$\gamma$ (distance)	$G$
Mass = population
Pre-pandemic	0.373	0.364	1.375	e^14.224
Pandemic	0.384	0.411	1.710	e^15.950
Endemic	0.351	0.356	1.642	e^16.610
Mass = gross floor area
Pre-pandemic	0.829	0.731	1.545	e^−0.758
Pandemic	0.716	0.695	1.810	e^3.279
Endemic	0.719	0.661	1.779	e^3.806

Distance exponent $\gamma$ rose in the pandemic and has come down only a little since: people became more sensitive to travel distance and have stayed so. In plain numbers, doubling the distance cut a flow to $2^{-1.375}\approx39$ % before the pandemic, to $2^{-1.710}\approx31$ % during it and to $2^{-1.642}\approx32$ % in the endemic stage (population version).
Mass exponents $\alpha,\beta$ fell with floor area: the size of origin and destination matters slightly less. With population they rose slightly during the pandemic and then fell below their pre-pandemic values in the endemic stage, preliminary evidence that the trip rates of different land-use types have changed.
The constant $G$ grew. In the log–log regression, $\ln G$ is the intercept; a larger $G$ means that factors other than population, floor area and distance have more influence on flows since the pandemic began.

6 · Summary

The laws are robust; the city they describe has shifted

Validity

All three laws hold

Gravity, radiation and visitation laws describe Singapore’s transit flows before, during and after the pandemic, with the visitation law best throughout.

Ranking

Gravity pulls ahead of radiation

Comparable before 2020; since then the fitted gravity model improved by 6–18 % while the parameter-free radiation model did not.

Inputs

Floor area beats population

For gravity and radiation models, land-use intensity predicts flows as well or better than residents; for the visitation law, population is better.

The structural changes show up in the fitted parameters, which can help planners rethink resilient urban mobility for the next decade. Two limitations: we used transit data only, so walking, private cars and personal mobility devices are missing (transit carries the large majority of urban trips in Singapore), and we applied the models as published rather than adapting them to directional transit flows. Deriving forms of these laws for the different stages of an epidemic is left for future work.

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